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A conservative difference scheme with optimal pointwise error estimates for twodimensional space fractional nonlinear Schrödinger equations Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210728
Hongling Hu, Xianlin Jin, Dongdong He, Kejia Pan, Qifeng ZhangIn this paper, a linearized semiimplicit finite difference scheme is proposed for solving the twodimensional (2D) space fractional nonlinear Schrödinger equation (SFNSE). The scheme has the property of mass and energy conservation at the discrete level, with an unconditional stability and a secondorder accuracy for both time and spatial variables. The main contribution of this paper is an optimal

Analysis of a momentum conservative mixedFEM for the stationary Navier–Stokes problem Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210705
Jessika Camaño, Carlos García, Ricardo OyarzúaIn this paper, we propose and analyze a new momentum conservative mixed finite element method for the Navier–Stokes problem posed in nonstandard Banach spaces. Our approach is based on the introduction of a pseudostress tensor relating the velocity gradient with the convective term, leading to a mixed formulation where the aforementioned pseudostress tensor and the velocity are the main unknowns of

Linearized and decoupled structurepreserving finite difference methods and their analyses for the coupled Schrödinger–Boussinesq equations Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210624
Dingwen Deng, Qiang WuIn this paper, a threelevel finite difference method (FDM), which preserves energy and mass conservative laws, is first derived for onedimensional (1D) nonlinear coupled Schrödinger–Boussinesq equations (NCSBEs). Using the discrete energy analysis method, error estimations have been proven to be in L2, H1, and L∞norms, respectively. Secondly, this energy and masspreserving FDM (EMFDM) is generalized

Error estimate of a finite element method for an optimal control problem with corner singularity using the stress intensity factor Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210720
Seokchan Kim, HyungChun LeeWe consider an optimal control problem for the Poisson equation on a nonconvex polygonal domain with the corner singularity. Previously, we proposed a novel algorithm for the accurate numerical solution for the Poisson equation on a polygonal domain with the domain singularity. Then, we investigated the error estimate and its efficient procedure for the numerical algorithm. In this article, we propose

On the application of a Krylov subspace spectral method to poroacoustic shocks in inhomogeneous gases Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210719
James V. Lambers, Pedro M. JordanPoroacoustic shocks in inhomogeneous gases are numerically simulated using Krylov subspace spectral (KSS) methods; specifically, existing KSS methods are modified to use basis functions tailored to the assumed density profile of the gas, and to handle the nonhomogeneous boundary condition used to insert the shockinducing signal. The simulations presented demonstrate that KSS methods are effective

A positivitypreserving and energy stable scheme for a quantum diffusion equation Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210717
Xiaokai Huo, And Hailiang LiuWe propose a new fullydiscretized finite difference scheme for a quantum diffusion equation, in both one and two dimensions. This is the first fullydiscretized scheme with proven positivitypreserving and energy stable properties using only standard finite difference discretization. The difficulty in proving the positivitypreserving property lies in the lack of a maximum principle for fourth order

A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210708
Yuanyuan Zhang, Xiaoping LiuIn this article, we construct and analyze a residualbased a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error

Ultraconvergence of finite element method by Richardson extrapolation for elliptic problems with inhomogeneous boundary conditions Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210708
Wenming He, Ren Zhao, Yong CaoIn this article, Richardson extrapolation technique is employed to investigate the local ultraconvergence properties of Lagrange finite element method using piecewise polynomials of degrees () for the second order elliptic problem with inhomogeneous boundary. A sequence of special graded partition are proposed and a new interpolation operator is introduced to achieve order local ultraconvergence for

Local and parallel finite element methods based on twogrid discretizations for unsteady convection–diffusion problem Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210705
Qingtao Li, Guangzhi DuIn this article, some local and parallel finite element methods are proposed and investigated for the timedependent convection–diffusion problem. With backward Euler scheme for the temporal discretization, the basic idea of the present methods is that for a solution to the considered equations, low frequency components can be approximated well by a relatively coarse grid and high frequency components

The BDF2 FDM for the fourthorder equations with the multiterm RL fractional integral kernels Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210705
Yuan Liu, Haixiang Zhang, Xuehua Yang, Yanling LiuIn this paper, we formulated the finite difference method for the fourth order integrodifferential equation with the RiemannLiouville multiterm fractional integral kernels. The formally twostep backward differentiation formula method and secondorder convolution quadrature are used in time. The and norm stability and convergence at each time level are given. Numerical results show that our scheme

Operator splitting for the fractional Kortewegde Vries equation Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210705
Rajib Dutta, Tanmay SarkarOur aim is to analyze operator splitting for the fractional Kortewegde Vries (KdV) equation, , , where is a nonlocal operator with . Under the appropriate regularity of the initial data, we demonstrate the convergence of approximate solutions obtained by the Godunov and Strang splitting. Obtaining the Lie commutator bound, we show that for the Godunov splitting, first order convergence in is obtained

Analysis of the parareal approach based on discontinuous Galerkin method for timedependent Stokes equations Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210702
Jun Li, YaoLin Jiang, Zhen MiaoThis paper analyzes a parareal approach based on discontinuous Galerkin (DG) method for the timedependent Stokes equations. A class of primal discontinuous Galerkin methods, namely variations of interior penalty methods, are adopted for the spatial discretization in the parareal algorithm (we call it parareal DG algorithm). We study three discontinuous Galerkin methods for the timedependent Stokes

Superconvergence analysis of an energy stable scheme with three step backward differential formulafinite element method for nonlinear reaction–diffusion equation Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210702
Junjun WangA three step backward differential formula scheme is proposed for nonlinear reaction–diffusion equation and superconvergence results are studied with Galerkin finite element method unconditionally. Energy stability is testified for the constructed scheme with an artificial term. Splitting technique is utilized to get rid of the ratio between the time step size and the subdivision parameter . Temporal

The divergencefree nonconforming virtual element method for the Navier–Stokes problem Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210702
Bei Zhang, Jikun Zhao, Meng LiWe present the divergencefree nonconforming virtual element method for the Navier–Stokes problem. By using a gradient projection operator, we construct a nonconforming virtual element that allows us to compute the L2projection. The nonconforming virtual element provides the exact divergencefree approximation to the velocity and is proved to be convergent with the optimal convergence rate. Finally

Analysis and numerical simulation of cross reaction–diffusion systems with the Caputo–Fabrizio and Riesz operators Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210513
Kolade M. OwolabiThe evolutionary dynamics of cross‐reaction–diffusion equations of predator–prey type are investigated in the sense of fractional operator. In the models, we replace the classical time and spatial derivatives with the Caputo–Fabrizio and Riesz fractional derivatives, respectively. The nature of the resulting problem (is nonlinear, nonlocal, and nonsingular) do not either admit a closed form solution

Numerical approximations of chromatographic models Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210505
Farid Bozorgnia, Sonia Seyed AllaeiA numerical scheme based on modified method of characteristics with adjusted advection (MMOCAA) is proposed to approximate the solution of the system liquid chromatography with multi components case. For the case of one component, the method preserves the mass. Various examples and computational tests numerically verify the accuracy and efficiency of the approach.

Learning parameters of a system of variable order fractional differential equations Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210430
Abhishek Kumar Singh, Mani Mehra, Samarth GulyaniWe introduce a machine learning framework that uses the differential evolution algorithm in combination with Adam–Bashforth–Moulton method to learn the parameters in a system of variable order fractional differential equations. In this work, we present out developments with regards to taking care of a class of problem: data‐driven discovery of system of variable order fractional differential equations

An effective relaxed alternating procedure for Cauchy problem connected with Helmholtz Equation Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210429
Karzan A. Berdawood, Abdeljalil Nachaoui, Mourad Nachaoui, Fatima AboudThis paper is concerned with the Cauchy problem for the Helmholtz equation. Recently, some new works asked the convergence of the well‐known alternating iterative method. Our main result is to propose a new alternating algorithm based on relaxation technique. In contrast to the existing results, the proposed algorithm is simple to implement, converges for all choice of wave number, and it can be used

A numerical technique based on B‐spline for a class of time‐fractional diffusion equation Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210429
Pradip Roul, V. M. K. Prasad Goura, Roberto CavorettoThis paper presents an efficient numerical technique for solving a class of time‐fractional diffusion equation. The time‐fractional derivative is described in the Caputo form. The L1 scheme is used for discretization of Caputo fractional derivative and a collocation approach based on sextic B‐spline basis function is employed for discretization of space variable. The unconditional stability of the

Partial differential integral equation model for pricing American option under multi state regime switching with jumps Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210427
Muhammad Yousuf, Abdul Q. M. KhaliqIn this paper, we consider a two dimensional partial differential integral equation (PDIE) model for pricing American option. A nonlinear rationality parameter function for two asset problems is introduced to deal with the free boundary. The rationality parameter function is added in the PDIEs used for pricing American option problems under multi‐state regime switching with jumps. The resulting two

On the sparse multiscale representation of 2‐D Burgers equations by an efficient algorithm based on multiwavelets Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210427
Behzad Nemati Saray, Mehrdad Lakestani, Mehdi DehghanIn this work, we design, analyze, and test the multiwavelets Galerkin method to solve the two‐dimensional Burgers equation. Using Crank–Nicolson scheme, time is discretized and a PDE is obtained for each time step. We use the multiwavelets Galerkin method for solving these PDEs. Multiwavelets Galerkin method reduces these PDEs to sparse systems of algebraic equations. The cost of this method is proportional

Magnetohdrodnamics nanofluid flow of shaped nanoparticles over a porous stretching wall and slip effect Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210419
Irfan Rashid, Muhammad Sagheer, Shafqat HussainIn this study, we analyze the magnetohydrodynamic flow of magnetite‐engine oil nanofluid in the presence of nonidentical shaped nanoparticles subject to the porous medium and velocity slip effect. Energy analysis is carried out with the Ohmic heating and thermal radiation impacts. The system of partial differential equations are transformed into the system of ordinary differential equations using similarity

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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) Pub Date : 20210126
Rodrigo L. R. Madureira, Mauro A. Rincon, Marcello G. TeixeiraCoupled parabolichyperbolic 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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

On some generalized integral inequalities for functions whose second derivatives in absolute values are convex Numer. Methods Partial Differ. Equ. (IF 3.009) 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.

A superlinear convergence scheme for the multiterm and distributionorder fractional wave equation with initial singularity Numer. Methods Partial Differ. Equ. (IF 3.009) Pub Date : 20210122
Jianfei Huang, Jingna Zhang, Sadia Arshad, Yifa TangIn this paper, a superlinear convergence scheme for the multiterm and distributionorder fractional wave equation with initial singularity is proposed. The initial singularity of the solution of the multiterm time fractional partial differential equation often generate a singular source, it increases the difficulty to numerically solve the equation. Thus, after discretizing the spatial distributionorder

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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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

Perturbation based analytical solutions of non‐Newtonian differential equation with heat and mass transportation between horizontal permeable channel Numer. Methods Partial Differ. Equ. (IF 3.009) 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 3.009) 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

A noniterative domain decomposition method for the interaction between a fluid and a thick structure Numer. Methods Partial Differ. Equ. (IF 3.009) 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 noniterative, domain decomposition

Combination of Shehu decomposition and variational iteration transform methods for solving fractional third order dispersive partial differential equations Numer. Methods Partial Differ. Equ. (IF 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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 3.009) 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

A variation of distance domination in composite networks Numer. Methods Partial Differ. Equ. (IF 3.009) 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

Weakly symmetric stress equilibration and a posteriori error estimation for linear elasticity Numer. Methods Partial Differ. Equ. (IF 3.009) 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 displacementpressure approximation computed with a stable finite element pair. Our focus is on the TaylorHood combination of continuous