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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

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

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

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

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

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).

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

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

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,

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 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

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

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

Analytical and numerical techniques for initial‐boundary value problems of Kolmogorov–Petrovsky–Piskunov equation Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201218
Ben Wongsaijai; Tuğba Aydemir; Turgut Ak; Sharanjeet DhawanIn this work, we are interested in finding exact and numerical solutions of well‐known Kolmogorov–Petrovsky–Piskunov (KPP) equation. Here, we introduce modified extended tanh method for finding the exact solutions of KPP equation and an average linear finite difference scheme for numerical investigations. It has been observed that the numerical scheme so employed is stable and accurate enough to produce

Sharp error estimates of a fourth‐order compact scheme for a Poisson interface problem Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201217
Haixia Dong; Wenjun Ying; Jiwei ZhangA simple and efficient fourth‐order kernel‐free boundary integral method was recently proposed by Xie and Ying for constant coefficients elliptic PDEs on complex domains. This method is constructed by a compact finite difference scheme and works efficiently with fourth‐order accuracy in the maximum norm. But it is challenging to present the sharp error analysis of the resulting approach since the local

An artificial neural network‐based method for the optimal control problem governed by the fractional parabolic equation Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201217
Majid Darehmiraki; Arezou Rezazadeh; Ali AhmadianIn this paper, we propose an artificial neural network model (ANN) to solve a partial differential equation (PDE) constrained optimization problem. Here, the discretize then optimize approach is used. At first, the Legendre polynomials are used to discretize the optimization problem and transform it into a quadratic optimization problem with linear constraint. Then an ANN model is proposed to solve

Finite element method with the total stress variable for Biot's consolidation model Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201217
Wenya Qi; Padmanabhan Seshaiyer; Junping WangIn this work, semi‐discrete and fully discrete error estimates are derived for the Biot's consolidation model described using a three‐field finite element formulation. These fields include displacements, total stress and pressure. The model is implemented using a backward Euler discretization in time for the fully discrete scheme and validated for benchmark examples. Computational experiments are presented

Accurate numerical integration for the quadrilateral and hexahedral finite elements Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201216
Ziqing Xie; Shangyou ZhangThe numerical integration for the bilinear form of quadrilateral or hexahedral finite elements can never be exact. It is discovered that the standard Gauss‐Legendre integration is exact if one of the two Qk polynomials in the bilinear form is a Pk polynomial. Based on this observation, it is proved the Qk finite elements, under practical numerical integration, retain the optimal order of convergence

Fourth‐order compact scheme based on quasi‐variable mesh for three‐dimensional mildly nonlinear stationary convection–diffusion equations Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201215
Navnit Jha; Bhagat SinghA new family of compact schemes of increased accuracy using quasi‐variable mesh is presented for determining approximate solutions to the three‐space dimensions mildly nonlinear convection dominated diffusion equations. The main thought behind the proposed scheme is to get uniformly distributed local truncation error, which otherwise not possible in case of finite‐difference discretization using constant

Numerical solution of singularly perturbed 2D parabolic initial‐boundary‐value problems based on reproducing kernel theory: Error and stability analysis Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201214
Mojtaba Fardi; Mehdi GhasemiThe main aim of this article is to propose two computational approaches on the basis of the reproducing kernel Hilbert space method for solving singularly perturbed 2D parabolic initial‐boundary‐value problems. For each approach, the solution in reproducing kernel Hilbert space is constructed with series form, and the approximate solution um is given as an m‐term summation. Furthermore, convergence

An optimized compact reconstruction weighted essentially non‐oscillatory scheme for advection problems Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201212
Bijin Liu; Ching‐Hao Yu; Ruidong AnThis paper presents an optimized compact reconstruction weighted essentially non‐oscillatory scheme without dissipation errors (OCRWENO‐LD) for solving advection problems. The construction procedure of this optimized scheme without dissipation errors is as follows: (1) We first design a high‐order compact difference scheme with four general weights connecting four low‐order compact stencils. The four

Asymptotic behavior of the solution of a singularly perturbed general boundary value problem with boundary jumps Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201212
Duisebek N. Nurgabyl; Alpamys B. UaissovIt is known that the study of boundary value and mixed problems for integrable linear equations encounters significant difficulties of a fundamental nature. Exceptions are problems with boundary conditions of a special type, which are often called integrable or linearizable. The purpose of this article is to study the asymptotic behaviors of solutions of singularly perturbed general boundary value

Results on approximate controllability of neutral integro‐differential stochastic system with state‐dependent delay Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201212
C. Dineshkumar; R. Udhayakumar; V. Vijayakumar; Kottakkaran Sooppy NisarThis article is mainly focusing on the approximate controllability of neutral integro‐differential stochastic equations with state‐dependent delay. The main results of this article are proved by applying some ideas about the semigroup theory and resolvent operators. At first, the investigation about the existence of a mild solution and then we discuss the approximate controllability of the considered

Global and local structure‐based influential nodes identification in wheel‐type networks Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201211
Murat Erşen BerberlerNetwork theory has been widely used to describe complex systems in the real world. Identifying the influential nodes in a network is one of the most important topic in the research of network theory. Identification of influential nodes in a network is a significant and challenging task since influential nodes act as a hub for information transmission in a command and control network, however it is

Numerical investigations on COVID‐19 model through singular and non‐singular fractional operators Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201211
Sunil Kumar; R. P. Chauhan; Shaher Momani; Samir HadidNowadays, the complete world is suffering from untreated infectious epidemic disease COVID‐19 due to coronavirus, which is a very dangerous and deadly viral infection. So, the major desire of this task is to propose some new mathematical models for the coronavirus pandemic (COVID‐19) outbreak through fractional derivatives. The adoption of modified mathematical techniques and some basic explanation

A half‐inverse problem for singular diffusion operator with certain boundary conditions Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201211
Abdullah Ergün; Rauf AmirovIn this paper, we studied the half inverse spectral problem for singular diffusion operator with certain boundary conditions. The discontinuity function in this operator is defined as and α > 0, α ≠ 1, β > 0, β ≠ 1 and a1, a2 ∈ (0, π), , . We prove that the potential functions p(x) and q(x) are determined uniquely by using the Yang–Zettl and Hocstadt–Lieberman methods. We examine that if potential

A decoupled stabilized finite element method for the dual‐porosity‐Navier–Stokes fluid flow model arising in shale oil Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201211
Liang Gao; Jian LiIn this paper, we consider the decoupled stabilized finite element method for the dual‐porosity‐Navier–Stokes model coupling the free flow region and the microfracture‐matrix system by using four interface conditions on the interface. The stabilized finite element method is decoupled in two levels, and it allows the coupling problem to be divide into three subproblems in a non‐iterative manner, which

Computational examination of Casson nanofluid due to a non‐linear stretching sheet subjected to particle shape factor: Tiwari and Das model Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201211
Wasim Jamshed; Vivek Kumar; Vikash KumarIn this research, heat transfer along with entropy of an unsteady non‐Newtonian Casson nanofluid flow is studied. The fluid is positioned over a stretched flat surface moving non‐uniformly. The nanofluid is analyzed for its flow and heat transport properties by subjecting it to a slippery surface, which is convectively heated. The governing mathematical equations describing the physical characteristics

Numerical solutions of fractional parabolic equations with generalized Mittag–Leffler kernels Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201211
Abedel‐Karrem Alomari; Thabet Abdeljawad; Dumitru Baleanu; Khaled M. Saad; Qasem M. Al‐MdallalIn this article, we investigate the generalized fractional operator Caputo type (ABC) with kernels of Mittag–Lefller in three parameters and its fractional integrals with arbitrary order for solving the time fractional parabolic nonlinear equation. The generalized definition generates infinitely many problems for a fixed fractional derivative α. We utilize this operator with homotopy analysis method

A simplified two‐level subgrid stabilized method with backtracking technique for incompressible flows at high Reynolds numbers Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201210
Xiaocheng Yang; Yueqiang Shang; Bo ZhengBased on finite element discretization, a simplified two‐level subgrid stabilized method with backtracking technique is proposed for the steady incompressible Navier–Stokes equations at high Reynolds numbers. The method combines the best algorithmic characteristics of the standard two‐level method with backtracking technique and subgrid stabilized method. In this method, we first solve a fully nonlinear

Some new integral inequalities associated with generalized proportional fractional operators Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201208
Erhan Set; Barış Çelik; Emrullah Aykan Alan; Ahmet Ocak AkdemirThe main objective of this paper is to develop certain type of fractional integral inequalities using generalized proportional fractional integral operator.

Results on approximate controllability of Sobolev type fractional stochastic evolution hemivariational inequalities Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201208
V. Vijayakumar; R. Udhayakumar; Sumati Kumari Panda; Kottakkaran Sooppy NisarIn our article, we primarily concentrate on the approximate controllability results for Sobolev type fractional stochastic evolution hemivariational inequalities. By applying the facts related to fractional calculus, and fixed‐point technique, the principal results are proved. Initially, we are concentrating the existence and continue to prove the controllability of the fractional evolution system

On Hosoya Index and Merrifield‐Simmons Index of trees with given domination number Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201208
Bünyamin ŞahinThe Hosoya index and the Merrifield‐Simmons index are two important molecular descriptors in chemical graph theory. The Hosoya index is defined as the total number of matchings of the graph and the Merrifield‐Simmons index is defined as the total number of independent sets of the graph. In this paper, the author obtains the extremal values of the Hosoya index and the Merrifield‐Simmons index of trees

Fast preconditioned iterative methods for fractional Sturm–Liouville equations Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201207
Lei Zhang; Guo‐Feng Zhang; Zhao‐Zheng LiangIn this paper, we have considered fast solutions of the linear system arising from the fractional Sturm–Liouville problem, whose coefficient matrix contains the product of Toeplitz‐like matrices. Based on suitable circulant approximations of the related coefficient matrix, we establish a matching preconditioner of matrix‐free form. In theory, the spectrum of the preconditioned matrix is shown to cluster

Numerical simulations for the predator–prey model as a prototype of an excitable system Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201207
Mostafa M. A. Khater; Bandar Almohsen; Dumitru Baleanu;This research paper investigates the numerical solutions of the predator–prey model through five recent numerical schemes (Adomian decomposition, El Kalla, cubic B‐spline, extended cubic B‐spline, exponential cubic B‐spline). We investigate the obtained computational solutions via the modified Khater methods. This model is considered as a well‐known bimathematical model to describe the prototype of

On the dynamics of strong Langmuir turbulence through the five recent numerical schemes in the plasma physics Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201204
Mostafa M. A. KhaterThis paper discusses the numerical solutions of the nonlinear Klein–Gordon–Zakharov model by the use of five recent numerical schemes (Adomian decomposition, El‐kalla, cubic B‐spline, extended cubic B‐spline, and exponential cubic B‐spline). The object of this numerical analysis is to demonstrate the accuracy of the analytical solutions obtained using the generalized Khater system and also to display

A formally second‐order backward differentiation formula Sinc‐collocation method for the Volterra integro‐differential equation with a weakly singular kernel based on the double exponential transformation Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201204
Wenlin Qiu; Da Xu; Jing GuoThis paper presents a formally second‐order backward differentiation formula (BDF2) Sinc‐collocation method for solving the Volterra integro‐differential equation with a weakly singular kernel. In the time direction, the time derivative is discretized via the BDF2 and the second‐order convolution quadrature rule is used to approximate the Riemann–Liouville fractional integral term. Then a fully discrete

On rigorous computational and numerical solutions for the voltages of the electrified transmission range with the day yet distance Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201203
Mostafa M. A. Khater; Y. S. Hamed; Dianchen LuThis research article aims to get superabundant wave solutions of the fractional nonlinear space–time telegraph via two computational schemes (modified Khater (MK) method and simplest equation (SE) method) through a new fractional operator (Atangana–Baleanu [AB] fractional derivative). These solutions are used to calculate the boundary and initial conditions that allow applying the B‐spline collection

A robust multigrid method for one dimensional immersed finite element method Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201203
Saihua Wang; Feng Wang; Xuejun XuIn this paper, we propose a robust multigrid method for 1D immersed finite element method (IFEM). It is shown that the multigrid method is optimal, which means that the convergence rate of the multigrid method is not only independent of the mesh size h and mesh level L, but also independent of the jump of the discontinuous coefficients. Although we only consider 1D interface method, to the best of

Results on existence and controllability results for fractional evolution inclusions of order 1 < r < 2 with Clarke's subdifferential type Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201203
M. Mohan Raja; V. Vijayakumar; R. Udhayakumar; Kottakkaran Sooppy NisarIn our paper, we primarily concentrate on the existence and controllability results for fractional evolution inclusions of order 1 < r < 2 with Clarke's subdifferential type. By applying the facts related to the measure of noncompactness, fractional calculus, and fixed‐point technique, the principal results are proved. Initially, we are concentrating the existence and continue to prove the controllability

Optimal error estimates of fourth‐order compact finite difference methods for the nonlinear Klein–Gordon equation in the nonrelativistic regime Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201201
Teng Zhang; Tingchun WangTwo fourth‐order compact finite difference schemes including a Crank–Nicolson one and a semi‐implicit one are derived for solving the nonlinear Klein–Gordon equations in the nonrelativistic regime. The optimal error estimates and the strategy in choosing time step are rigorously analyzed, and the energy conservation in the discrete sense is also studied. Under proper assumption on the analytical solutions

Some special functions in orthogonal fuzzy bipolar metric spaces and their fixed point applications Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201201
Müzeyyen Sangurlu SezenIn this work, we synthesize orthogonal and bipolar metric issues and tried to deal with them in fuzzy metric spaces. We introduce a new concept of orthogonal fuzzy bipolar metric space and prove some fixed point theorems for some contractions in this space. Also, we provide some examples to illustrate the validity of the results obtained in the paper.

Error estimation for second‐order partial differential equations in nonvariational form Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201201
Jan Blechschmidt; Roland Herzog; Max WinklerSecond‐order partial differential equations (PDEs) in nondivergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton–Jacobi–Bellman equations in the context of stochastic optimal control, or as the linearization of fully nonlinear second‐order PDEs. The nondivergence form in these problems is natural. If the coefficients of the diffusion matrix

Coloring in graphs of twist knots Numer. Methods Partial Differ. Equ. (IF 2.236) Pub Date : 20201201
Abdulgani ŞahinLet Tn be a twist knot with n half‐twists and Gn be the graph of Tn. The closed neighborhood N[v] of a vertex v in Gn, which included at least one colored vertex for each color in a proper n‐coloring of Gn, is called a rainbow neighborhood. There are different types of graph coloring in the literature. We consider some of these types in here. In this paper, we determine the chromatic number of graphs