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An inverse problem of identifying the time‐dependent potential in a fourth‐order pseudo‐parabolic equation from additional condition Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210408
Mousa J. Huntul, Mohammad Tamsir, Neeraj DhimanThe aim of this work is to identify numerically, for the first time, the time‐dependent potential coefficient in a fourth‐order pseudo‐parabolic equation with nonlocal initial data, nonlocal boundary conditions, and the boundary data as overdetermination condition. This problem emerges significantly in the modeling of various phenomena in physics and engineering. From literature we already know that

A fully‐mixed finite element method for the coupling of the Navier–Stokes and Darcy–Forchheimer equations Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210126
Sergio Caucao, Gabriel N. Gatica, Felipe SandovalIn this work we present and analyze a fully‐mixed formulation for the nonlinear model given by the coupling of the Navier–Stokes and Darcy–Forchheimer equations with the Beavers–Joseph–Saffman condition on the interface. Our approach yields non‐Hilbertian normed spaces and a twofold saddle point structure for the corresponding operator equation. Furthermore, since the convective term in the Navier–Stokes

Accurate and efficient algorithms with unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn equations Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210123
Zhengguang Liu, Xiaoli Li, Jian HuangComparing with the classic phase filed models, the fractional models such as time fractional Allen–Cahn and Cahn–Hilliard equations are equipped with Caputo fractional derivative and can describe more practical phenomena for modeling phase transitions. In this paper, we construct two accurate and efficient linear algorithms for the time fractional Cahn–Hilliard and Allen–Cahn equations with general

Finite difference technique to solve a problem of generalized thermoelasticity on an annular cylinder under the effect of rotation Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210123
Abdelmooty M. Abd‐Alla, Sayed M. Abo‐Dahab, Araby A. KilanyThis article estimates the action of rotation on a generalized thermoelasticity model which contains one thermal relaxation time for an infinitely long, annular, isotropic cylinder with temperature‐dependent physical properties. This is numerically solved using the finite difference technique under the effect of rotation, and the effect of decaying heat flux on the obtained components is graphically

A numerical method for solving variable‐order fractional diffusion equations using fractional‐order Taylor wavelets Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210123
Thieu N. Vo, Mohsen Razzaghi, Phan Thanh ToanThis paper aims to provide a new numerical method for solving variable‐order fractional diffusion equations. The method is constructed using fractional‐order Taylor wavelets. By using the regularized beta function, a formula for computing the exact value of Riemann‐Liouville fractional integral operator of the fractional‐order Taylor wavelets is given. The Taylor wavelets properties and the formula

A new and efficient numerical method based on shifted fractional‐order Jacobi operational matrices for solving some classes of two‐dimensional nonlinear fractional integral equations Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210125
Khosrow Maleknejad, Jalil Rashidinia, Tahereh EftekhariThe aim of this paper is to present a new and efficient numerical method to approximate the solutions of two‐dimensional nonlinear fractional Fredholm and Volterra integral equations. For this aim, the two‐variable shifted fractional‐order Jacobi polynomials are introduced and their operational matrices of fractional integration and product are derived. These operational matrices and shifted fractional‐order

Nonconforming finite element method for coupled Poisson–Nernst–Planck equations Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210121
Xiangyu Shi, Linzhang LuA nonconforming finite element method (FEM) is developed and investigated for the coupled Poisson–Nernst–Planck (PNP) equations with low order element. Then, by use of the special properties of this element, that is, the interpolation operator is equivalent to its projection operator, and the consistency error estimate can reach order of O(h2) which is one order higher than that of its interpolation

An explicit order 2 scheme for the strong approximation of Stratonovich stochastic differential equations with scalar noise Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210201
Hande Günay AkdemirA new class of stochastic Runge–Kutta (SRK) methods for the strong approximation of Stratonovich stochastic ordinary differential equations (SODEs) is presented. The proposed method is an alternative to the method of Xiao and Tang (Numer. Algor. 72: 259–296, 2016) and converges with order 2 in the strong sense. To validate the efficiency and to compare with some known methods, numerical simulations

Higher‐order explicit schemes based on the method of characteristics for hyperbolic equations with crossing straight‐line characteristics Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210322
Taras I. Lakoba, Jeffrey S. JewellWe develop method of characteristics schemes based on explicit Runge–Kutta and pseudo‐Runge–Kutta third‐ and fourth‐order solvers along the characteristics. Schemes based on Runge–Kutta solvers are found to be strongly unstable for certain physics‐motivated models. In contrast, schemes based on pseudo‐Runge–Kutta solvers are shown to be only weakly unstable for periodic boundary conditions and essentially

An efficient numerical approach for fractional multidimensional diffusion equations with exponential memory Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201120
Jagdev Singh, Devendra Kumar, Sunil Dutt Purohit, Aditya Mani Mishra, Mahesh BohraIn this article, we suggest a numerical approach based on q‐homotopy analysis Elzaki transform method (q‐HAETM) to solve fractional multidimensional diffusion equations which represents density dynamics in a material undergoing diffusion. We take the noninteger derivative in the Caputo–Fabrizio kind. The proposed method, q‐HAETM is an advanced adaptation in q‐HAM and Elzaki transform method which makes

Legendre wavelet collocation method for fractional optimal control problems with fractional Bolza cost Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201120
Nitin Kumar, Mani MehraThis paper exhibits a numerical method for solving general fractional optimal control problems involving a dynamical system described by a nonlinear Caputo fractional differential equation, associated with a fractional Bolza cost composed as the aggregate of a standard Mayer cost and a fractional Lagrange cost given by a Riemann–Liouville fractional integral. By using the Lagrange multiplier within

A new approach for the qualitative study of vector born disease using Caputo–Fabrizio derivative Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201229
Fazal Haq, Ibrahim Mahariq, Thabet Abdeljawad, Nabil MalikiIn this manuscript, we investigate the existence and the semi‐analytical solutions of the fractional‐order vector‐born disease model using the Caputo–Fabrizio fractional derivative. In this study, we have developed existence results about the solution for the problem under consideration using the results of fixed‐point theory. On the other hand, the semi‐analytical results were obtained via Laplace

Numerical methods for a problem of thermal diffusion in elastic body with moving boundary Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210126
Rodrigo L. R. Madureira, Mauro A. Rincon, Marcello G. TeixeiraCoupled parabolic‐hyperbolic system often appears in the studies of thermoelasticity, magnetoelasticity, biological problems and radiation hydrodynamics with high temperature. In this paper, we investigate a problem of thermal diffusion in elastic body with moving boundary. Three numerical methods, two uncoupled and one coupled, all with quadratic convergence order in time and space, are presented

Al2O3‐47 nm and Al2O3‐36 nm characterizations of nonlinear differential equations for biomedical applications: Magnetized peristaltic transport Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210125
Shahid Farooq, Muhammad Ijaz Khan, Faris Alzahrani, Aatef HobinyCurrent research models the Al2O3 47nm and Al2O3 36nm nanoparticles transportation through peristalsis with entropy optimization. Conservation laws for mass, momentum and energy are used to model the present flow situation. These equations elaborates the magnetohydrodynamics, Hall, thermal radiation, Joule heating, heat generation and absorption. Convective heat transfer impacts are studied at channel

New formulas of the high‐order derivatives of fifth‐kind Chebyshev polynomials: Spectral solution of the convection–diffusion equation Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210125
Waleed M. Abd‐Elhameed, Youssri H. YoussriThis paper is dedicated to deriving novel formulae for the high‐order derivatives of Chebyshev polynomials of the fifth‐kind. The high‐order derivatives of these polynomials are expressed in terms of their original polynomials. The derived formulae contain certain terminating 4F3(1) hypergeometric functions. We show that the resulting hypergeometric functions can be reduced in the case of the first

The analytical solution of fractional‐order Whitham–Broer–Kaup equations by an Elzaki decomposition method Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210123
Nehad Ali Shah, Jae Dong ChungIn this article, the Elzaki decomposition method is used to evaluate the solution of fractional‐order Whitham–Broer–Kaup equations. With the help of Elzaki transform coupled with Adomian decomposition method, an iterative procedure is established to investigate approximate solution to the suggested coupled scheme of nonlinear partial fractional differential equations. The solution of some illustrative

Application of direct meshless local Petrov–Galerkin method for numerical solution of stochastic elliptic interface problems Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210122
Mostafa Abbaszadeh, Mehdi Dehghan, Amirreza Khodadadian, Clemens HeitzingerA truly meshless numerical procedure to simulate stochastic elliptic interface problems is developed. The meshless method is based on the generalized moving least squares approximation. This method can be implemented in a straightforward manner and has a very good accuracy for solving this kind of problems. Several realistic examples are presented to investigate the efficiency of the new procedure

A superlinear convergence scheme for the multi‐term and distribution‐order fractional wave equation with initial singularity Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210122
Jianfei Huang, Jingna Zhang, Sadia Arshad, Yifa TangIn this paper, a superlinear convergence scheme for the multi‐term and distribution‐order fractional wave equation with initial singularity is proposed. The initial singularity of the solution of the multi‐term time fractional partial differential equation often generate a singular source, it increases the difficulty to numerically solve the equation. Thus, after discretizing the spatial distribution‐order

On some generalized integral inequalities for functions whose second derivatives in absolute values are convex Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210122
Erhan Set, Alper EkinciIn this article, general integral inequalities are obtained for functions whose absolute value of the second derivative is convex. These inequalities are more general versions of some results in the literature and we recaptured these results with the selection of special parameters. In the study, graphs are also used to compare the inequalities that occur with the change of the µ parameter.

New discussion on approximate controllability results for fractional Sobolev type Volterra‐Fredholm integro‐differential systems of order 1 < r < 2 Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210121
V. Vijayakumar, Chokkalingam Ravichandran, Kottakkaran Sooppy Nisar, Kishor D. KuccheIn our article, we are primarily concentrating on approximate controllability results for fractional Sobolev type Volterra‐Fredholm integro‐differential inclusions of order 1 < r < 2. By applying the results and ideas belongs to the cosine function of operators, fractional calculus and fixed point approach, the main results are established. Initially, we establish the approximate controllability of

On the asymptotic behavior of a second‐order general differential equation Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210120
Fatih SayStudying ordinary or partial differential equations or integrals using traditional asymptotic analysis, unfortunately, fails to extract the exponentially small terms and fails to derive some of their asymptotic features. In this paper, we discuss how to characterize an asymptotic behavior of a singular linear differential equation by the methods in exponential asymptotics. This paper is particularly

Semitotal domination number of some graph operations Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210120
Zeliha Kartal Yıldız, Aysun AytaçA semitotal dominating set S (abbreviated semi‐TD‐set) of graph G = (V, E) is a subset such that S is a dominating set and each vertex in the S is within 2 distance from the another vertex of S. The semitotal domination number, denoted by γt2(G), is the minimum cardinality taken over all semitotal dominating sets of G. In this paper, we examine the semitotal domination number of graphs obtained by

Higher‐order algorithms for stable solutions of fractional time‐dependent nonlinear telegraph equations in space Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210120
Muhammad Usman, Muhammad Hamid, Moubin LiuIn this article, three novel algorithms are developed and successfully applied to investigate the stable solutions of time‐fractional nonlinear telegraph equations. Firstly, we presented the shifted Gegenbauer polynomials through appropriate transformations. The approximation of a function u(x, t) is defined via shifted Gegenbauer polynomials (SGPs) and then developed the operational matrices of

Mathematical modeling of bio‐magnetic fluid bounded within ciliated walls of wavy channel Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210120
Mubbashar Nazeer, Farooq Hussain, Sadia Iftikhar, Muhammad Ijaz Khan, K. Ramesh, Nasir Shehzad, Afifa Baig, Seifedine Kadry, Yu‐Ming ChuPeristaltic transport of couple stress fluid with heat transfer is investigated through flexible walls of the channel furnished with hair‐like structures. Locomotion of biological fluid is the result of the simultaneous propagation of metachronal waves (MCWs) and peristaltic waves. MCW emerges due to multi‐movement of cilia, while the elastic‐walls of the channel are responsible for the peristaltic

A non‐iterative domain decomposition method for the interaction between a fluid and a thick structure Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210120
Anyastassia Seboldt, Martina BukačThis work focuses on the development and analysis of a partitioned numerical method for moving domain, fluid–structure interaction problems. We model the fluid using incompressible Navier–Stokes equations, and the structure using linear elasticity equations. We assume that the structure is thick, that is, described in the same dimension as the fluid. We propose a non‐iterative, domain decomposition

Perturbation based analytical solutions of non‐Newtonian differential equation with heat and mass transportation between horizontal permeable channel Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210120
Mubbashar Nazeer, M. Ijaz Khan, Adila Saleem, Yu‐Ming Chu, Seifedine Kadry, M. Tahir RasheedA mathematical model is constructed in this investigation to examine the effects of heat and mass transfer in tangent‐hyperbolic fluid bounded within horizontal channel. The lower‐wall of channel is taken as heated. The dimensional momentum, energy and concentration equations are determined by defining a stress‐tensor of undertaken fluid (Tangent‐hyperbolic fluid). To calculate the solution, the system

Comparison between the new exact and numerical solutions of the Mikhailov–Novikov–Wang equation Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210120
Ahmet Bekir, Maha S. M. Shehata, Emad H. M. ZahranIn this article, we employ the Mikhailov–Novikov–Wang integrable equation (MNWIE) appearing by means of the perturbatives symmetry approach to the rating of integrable non‐evolutionary PDEs. The new exact soliton solutions of this equation which were not achieved before have been realized for the first time in the framework of the (G′/G)‐expansion method. In the same vein and parallel, the corresponding

Combination of Shehu decomposition and variational iteration transform methods for solving fractional third order dispersive partial differential equations Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210118
Yu‐Ming Chu, Ehab Hussein Bani Hani, Essam R. El‐Zahar, Abdelhalim Ebaid, Nehad Ali ShahIn this article, the fractional third‐order dispersive partial differential equations were investigated by using Shehu decomposition and variational iteration transform methods. The well known Riemann‐Liouville fraction integral, Caputo's fractional‐order derivative, Shehu transform for fractional‐order derivatives and Mittag‐Leffler function were used as the major basis of the methodology. The graphs

Sharp estimates of the unique solution for two‐point fractional boundary value problems with conformable derivative Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210118
Zaid Laadjal, Thabet Abdeljawad, Fahd JaradIn this work, we investigate the condition of the given interval which ensures the existence and uniqueness of solutions for two‐point boundary value problems within conformable‐type local fractional derivative. The method of analysis is obtained by the principle of contraction mapping. Furthermore, benefiting from calculating the integral of the Green's function, we are able to improve a recent result

MHD two‐phase flow of Jeffrey fluid suspended with Hafnium and crystal particles: Analytical treatment Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210116
Mubbashar Nazeer, Farooq Hussain, M. Ijaz Khan, Qasiar Shahzad, Yu‐Ming Chu, Seifedine KadryThis article offers a comparative investigation for Newtonian and non‐Newtonian multiphase flows drifting through an inclined channel. A non‐Newtonian Jeffrey fluid is used as the base fluid. However, Hafnium particles and crystal particles are considered to form two different kinds of two‐phase suspensions. Each flow comes under the influence of an external and transversely applied magnetic force

New extensions of Hermite–Hadamard inequalities via generalized proportional fractional integral Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210116
İlker Mumcu, Erhan Set, Ahmet Ocak Akdemir, Fahd JaradThe main aim this work is to give Hermite–Hadamard inequalities for convex functions via generalized proportional fractional integrals. We also obtained extensions of Hermite–Hadamard type inequalities for generalized proportional fractional integrals.

Convergence analysis of reproducing kernel particle method to elliptic eigenvalue problem Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210118
Hsin‐Yun Hu, Jiun‐Shyan ChenIn this work we aim to provide a fundamental theory of the reproducing kernel particle method for solving elliptic eigenvalue problems. We concentrate on the convergence analysis of eigenvalues and eigenfunctions, as well as the optimal estimations which are shown to be related to the reproducing degree, support size, and overlapping number in the reproducing kernel approximation. The theoretical analysis

Numerical solutions of the partial differential equations for investigating the significance of partial slip due to lateral velocity and viscous dissipation: The case of blood‐gold Carreau nanofluid and dusty fluid Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210115
Olubode Kolade Koriko, Kolawole S. Adegbie, Nehad Ali Shah, Isaac L. Animasaun, M. Adejoke OlotuThe dynamics of blood conveying gold nanoparticles (GNPs) are helpful to the health workers while air conveying dust particles over rockets is helpful to space scientists during the testing phase. However, little is known on the significance of thermal diffusivity in these aforementioned cases. In this report, the partial differential equation suitable to unravel the implication of increasing partial

Decatic B‐spline collocation scheme for approximate solution of Burgers' equation Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210114
Saumya R. Jena, Guesh S. GebremedhinA decatic B‐spline collocation technique is employed to compute the numerical result of a nonlinear Burgers' equation. The nonlinear term of Burgers' equation is locally linearized using Taylor series technique. The present method is effective for the approximate solution of Burgers' with a very small value of kinematic viscosity “a.” Some illustrated numerical experiments are taken into consideration

Effects of radiative heat flux and heat generation on magnetohydodynamics natural convection flow of nanofluid inside a porous triangular cavity with thermal boundary conditions Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210114
M. Waqas Nazir, Tariq Javed, Nasir Ali, Mubbashar NazeerWhen the nanoparticles are incorporated into the base fluid, the resultant fluid is known as nanofluid. Nanofluids have higher thermal efficiency as compared to base fluid. Some fluids have poor thermal conductivity like, water, air and ethylene glycol and oil. Thus, the thermal efficiency of the work can be increased by inserting the nanoparticles into base fluid. Furthermore, the nanoparticles can

Simple and efficient continuous data assimilation of evolution equations via algebraic nudging Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210114
Leo G. Rebholz, Camille ZerfasWe introduce, analyze, and test an interpolation operator designed for use with continuous data assimilation (DA) of evolution equations that are discretized spatially with the finite element method. The interpolant is constructed as an approximation of the L2 projection operator onto piecewise constant functions on a coarse mesh, but which allows nudging to be done completely at the linear algebraic

Weakly symmetric stress equilibration and a posteriori error estimation for linear elasticity Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210113
Fleurianne Bertrand, Bernhard Kober, Marcel Moldenhauer, Gerhard StarkeThis paper proposes and analyzes a posteriori error estimator based on stress equilibration for linear elasticity with emphasis on the behavior for (nearly) incompressible materials. It is based on an H(div)‐conforming, weakly symmetric stress reconstruction from the displacement‐pressure approximation computed with a stable finite element pair. Our focus is on the Taylor‐Hood combination of continuous

A variation of distance domination in composite networks Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210113
Vecdi Aytaç, Fatmana ŞentürkLet V be the set of vertex of a graph G. The set S is a dominating set, being a subset of the set V, if every vertex in the set V is in the set S, or if it is neighbor of a vertex in the set S. The number of elements of the set S with the least number of elements is the dominating number of graph G. In this study, we have worked on a type of dominating called porous exponential domination. In this

A novel approach for the solution of fractional diffusion problems with conformable derivative Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210111
Mine A. Bayrak, Ali Demir, Ebru OzbilgeThe truncated solution of space–time fractional differential equations, including conformable derivative is constructed by the help of residual power series method (RPSM). At the first step the space–time fractional differential equations are transformed into space fractional differential equations or time fractional differential equations by means of a specific transformation. Then the solutions are

Numerical analysis of Crank–Nicolson method for simplified magnetohydrodynamics with linear time relaxation Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210109
Gamze Yuksel, Simge K. ErogluThe Crank–Nicolson (CN) finite element method is examined with a linear time relaxation term in this study. The linear differential filter term is added to simplified magnetohydrodynamics (SMHD) equations for numerical regularization and it introduced SMHD linear time relaxation model (SMHDLTRM). The SMHDLTRM model is discretized by CN method in time and the finite element method in space. The stability

Assessment of boundary layer for flow of non‐Newtonian material induced by a moving belt with power law viscosity and thermal conductivity models Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210107
Mohsan Hassan, Kamel Al‐Khaled, Sami Ullah Khan, Iskander Tlili, Wathek ChammamThe non‐Newtonian fluids have become quite prevalent in industry and engineering for different applications. When these fluids flow over industrial equipment, a boundary layer phenomenon is developed due surface friction of equipment. In this work, a boundary layer phenomenon for two famous non‐Newtonian fluids namely pseudoplastic and dilatant over moving belt is discussed. The physical problem is

Quadratic B‐spline collocation method for time dependent singularly perturbed differential‐difference equation arising in the modeling of neuronal activity Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210105
Meenakshi Shivhare, Pramod Chakravarthy Podila, Higinio Ramos, Jesús Vigo‐AguiarIn this paper, we consider a time‐dependent singularly perturbed differential‐difference equation with small shifts arising in the field of neuroscience. The terms containing the delay and advance parameters are approximated by using the Taylor's series expansion. The continuous problem is semi‐discretized using the Crank–Nicolson finite difference method in the time direction on uniform mesh and quadratic

Lattice automorphism and zero‐divisor graphs of lattices Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210105
Alper ÜlkerLet ℒ be a bounded lattice and α : ℒ → ℒ be its automorphism. In this paper, we study zero‐divisor graph of ℒ with respect to an automorphism α. It is a simple undirected graph and denoted by Γα(ℒ). Some combinatorial structures such as coloring, diameter and girth were given for Γα(ℒ).

An improved numerical technique for distributed‐order time‐fractional diffusion equations Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20210105
Haniye Dehestani, Yadollah Ordokhani, Mohsen RazzaghiThis paper considers a novel numerical method based on Lucas‐fractional Lucas functions (L‐FL‐Fs) and collocation method for solving the distributed‐order time‐fractional diffusion equations. In the current investigation, we express the new computational process to gain the integral operational matrix for Lucas polynomials (LPs) and fractional Lucas functions (FLFs). The proposed method creates operational

Significance of bioconvection in flow of Williamson nano‐material confined by a porous radioactive Riga surface with convective Nield constrains Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201230
Iftikhar Ahmad, Samaira Aziz, Nasir Ali, Sami Ullah KhanThe improved thermal assessment of nano‐particles in presence of magnetic force, thermal radiation and activation energy involve dynamic applications in thermal engineering, industrial processes, and modern technologies. The bioconvection pattern in various nanoparticles attributes novel bio‐technology applications like bio‐fuels petroleum engineering, enzymes, bio‐sensors, and many more. On this end

Unconditionally optimal error estimates of BDF2 Galerkin method for semilinear parabolic equation Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201230
Huaijun Yang, Dongyang Shi, Li‐Tao ZhangIn this paper, a 2‐step backward differentiation formula (BDF2) Galerkin method is investigated for semilinear parabolic equation. More precisely, the second‐order time‐stepping scheme is used for time discretization and the piecewise linear continuous Galerkin method is employed for spatial discretization, respectively. Optimal error estimates in L2 and H1‐norms are obtained without any restriction

On the nondifferentiable exact solutions to Schamel's equation with local fractional derivative on Cantor sets Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201229
Behzad GhanbariThe various aspects of differential calculus are always on the path to progress and excellence, and these trends have been more highlighted in recent decades. More specifically, tremendous advances have been made in the field of fractional calculus. One of the main branches in this field is the local fractional derivative, which has been used successfully to describe many real‐world phenomena in science

A new stable finite difference scheme and its error analysis for two‐dimensional singularly perturbed convection–diffusion equations Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201229
Kamalesh Kumar, Pramod Chakravarthy PodilaThis work focuses on the numerical solution of two‐dimensional singularly perturbed convection–diffusion equations via a new stable finite difference (NSFD) scheme on a tensor product of two piecewise‐uniform Shishkin meshes. First, we convert the two‐dimensional equation into two one‐dimensional equations using the alternating direction implicit technique. A NSFD scheme has been developed using Taylor's

Numerical study and chaotic oscillations for aerodynamic model of wind turbine via fractal and fractional differential operators Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201229
Kashif Ali AbroThe aeroelastic analysis has become important for aerodynamical model of wind turbine in predicting the wind turbine; such phenomenon is based on aerodynamic performance to have accuracy and feasibility through modeling of fractal and fractional differential techniques. In this context, the mathematical modeling is developed based on fractal and fractional differential techniques for three‐dimensional

Computing the weighted neighbor isolated tenacity of interval graphs in polynomial time Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201229
Ersin Aslan, Mehmet A. TosunWeighted graphs in graph theory are created by weighing different values depending on the importance of connections or centers in a graph model. Networks can be modeled with graphs such that the devices and centers correspond to the vertices and connections correspond to the edges. In these networks, weight can be assigned to the vertices for the workload and importance of the devices and centers,

Two‐dimensional Haar wavelet based approximation technique to study the sensitivities of the price of an option Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201228
Devendra Kumar, Komal DeswalIn the present work, a two‐dimensional Haar wavelet method is proposed to study the sensitivities of the price of an option. The method is appropriate to study these sensitivities as it explicitly gives the values of all the derivatives of the solution. A Black–Scholes model for European style options is considered to analyze the physical and numerical aspects of the put and the call option Greeks

Ostrowski type inequalities for multiplicatively P‐functions Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201227
Huriye KadakalIn this paper, by using both the Hölder, power‐mean integral inequalities and Hölder‐İşcan, improved power‐mean integral inequalities that give approach better than Hölder and power‐mean inequalities respectively, some new Ostrowski type inequalities are derived for multiplicatively P‐function. The results obtained in both cases are compared and the results obtained using Hölder‐İşcan and improved

Numerical solution of q‐dynamic equations Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201227
Hamdy I. Abdel‐Gawad, Ali A. Aldailami, Khaled M. Saad, José F. Gómez‐AguilarThe variational iteration method (VIM) was used to find approximate numerical solutions of classical and fractional dynamical system equations. To the best of our knowledge, no work on the numerical treatment of q‐nonlinear dynamic systems NLDSs is done in the literature. This motivated us to study the numerical solutions of this problem. In this paper, the VIM is extended to find the numerical solutions

A non‐standard finite difference method for space fractional advection–diffusion equation Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201223
Ziting Liu, Qi WangIn this paper, a non‐standard finite difference scheme is developed to solve the space fractional advection–diffusion equation. By using Fourier–Von Neumann method, we prove that non‐standard finite difference scheme is unconditionally stable. We further discuss the convergence of numerical method and give the order of convergence. The numerical examples show that the non‐standard finite difference

A combined meshfree exponential Rosenbrock integrator for the third‐order dispersive partial differential equations Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201223
Hüseyin KoçakThe aim of this study is to propose a combined numerical treatment for the dispersive partial differential equations involving dissipation, convection and reaction terms with nonlinearity, such as the KdV‐Burgers, KdV and dispersive‐Fisher equations. We use the combination of the exponential Rosenbrock–Euler time integrator and multiquadric‐radial basis function meshfree scheme in space as a qualitatively

A class of new stable, explicit methods to solve the non‐stationary heat equation Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201223
Endre KovácsWe present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do not approximate the time derivatives by finite differences, but use constant‐neighbor and linear‐neighbor approximations to decouple the ordinary differential equations

A mixed finite element method for the Poisson problem using a biorthogonal system with Raviart–Thomas elements Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201221
Lothar Banz, Muhammad Ilyas, Bishnu P. Lamichhane, William McLean, Ernst P. StephanWe use a three‐field mixed formulation of the Poisson equation to develop a mixed finite element method using Raviart–Thomas elements. We use a locally constructed biorthogonal system for Raviart–Thomas finite elements to improve the computational efficiency of the approach. We analyze the existence, uniqueness and stability of the discrete problem and show an a priori error estimate. We also develop

Existence and controllability of nonlocal mixed Volterra‐Fredholm type fractional delay integro‐differential equations of order 1 < r < 2 Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201219
W. Kavitha Williams, V. Vijayakumar, R. Udhayakumar, Sumati Kumari Panda, Kottakkaran Sooppy NisarIn our article, we are primarily concentrating on existence and controllability of nonlocal mixed Volterra‐Fredholm type fractional delay integro‐differential equations of order 1 < r < 2. By applying the results and facts belongs to the cosine function of operators, fractional calculus, the measure of noncompactness and fixed point approach, the main results are established. Initially, we focus the

Results on approximate controllability of nondensely defined fractional neutral stochastic differential systems Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201218
C. Dineshkumar, R. UdhayakumarIn our article, we are primarily concentrating on approximate controllability results for nondensely defined fractional neutral stochastic differential systems. By applying the results and ideas belongs to fractional calculus, multivalued maps and fixed point approach, the main results are established. Initially, we establish the approximate controllability of the considered fractional system, then

Generalized differential quadrature scrutinization of an advanced MHD stability problem concerned water‐based nanofluids with metal/metal oxide nanomaterials: A proper application of the revised two‐phase nanofluid model with convective heating and through‐flow boundary conditions Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201218
Abderrahim Wakif, Rachid SehaquiThe present numerical investigation aimed to disclose the optimum characteristics of the magneto‐convection phenomenon that can be happened for Newtonian nanofluids in a horizontal planar configuration under the combined influence of an imposed convective heating and a uniform vertically applied through‐flow process at the permeable boundaries. In this regards, a realistic non‐homogeneous MHD convective