A meshfree method based on the radial basis functions for solution of two-dimensional fractional evolution equation

Ghehsareh, Hadi Roohani; Bateni, Sayna Heydari; Zaghian, Ali

doi:10.1016/j.enganabound.2015.06.009

Cited by 33 publications

(3 citation statements)

References 64 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[47][48][49] Various meshless techniques based on the RBFs have been developed and used for solving many types of fractional problems. [50][51][52][53][54][55][56][57][58][59] Very recently, Fu et al 60 employed the method of approximate particular solutions (MAPS) as an alternative of the RBFs for solving diffusion models with constant and variable order time-fractional derivatives.…”

Section: Introductionmentioning

confidence: 99%

The method of approximate particular solutions to simulate an anomalous mobile‐immobile transport process

Ghehsareh

Zaghian

Majlesi

2020

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

In the current work, a generalized mathematical model based on the Coimbra time fractional derivative of variable order, which describes an anomalous mobile‐immobile transport process in complex systems is investigated numerically. A robust numerical technique based on the meshfree strong form method combined with an efficient time‐stepping scheme is performed to compute the approximate solution of the problem with high accuracy. For this purpose, firstly, an effective implicit time discretization approach is used for discretizing the variable‐order time fractional problem in the time direction. Then a global meshless technique based on the method of approximate particular solutions is performed to fully discretize the model in the spatial domain. The validity and performance of the procedure to numerically simulate the proposed generalized solute transport model on regular and irregular domains are demonstrated through some numerical examples.

show abstract

Section: Introductionmentioning

confidence: 99%

The method of approximate particular solutions to simulate an anomalous mobile‐immobile transport process

Ghehsareh

Zaghian

Majlesi

2020

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…The meshless methods based on the RBFs are classified into two principle classes: RBFs meshless methods based on strong form such as and RBFs meshless methods based on weak forms such as radial point interpolation method [30][31][32][33][34][35][36][37]. Very recently, the meshless methods based on the RBFs have been widely used to investigate the numerical solutions of the various types of practical fractional problems [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54]. In the current work, an efficient numerical technique based on a combination of meshless local radial point interpolation method and a time discrete scheme would be discussed and formulated to approximate the solution of governing fractional model (1) with initial and boundary conditions (2).…”

Section: Introductionmentioning

confidence: 99%

Application of meshless local Petrov–Galerkin technique to simulate two-dimensional time-fractional Tricomi-type problem

Ghehsareh

Raei

Zaghian

2019

J Braz. Soc. Mech. Sci. Eng.

Self Cite

View full text Add to dashboard Cite

The paper is devoted to investigate the two-dimensional time-fractional Tricomi-type equation, which describes the anomalous process of nearly sonic speed gas dynamics. An efficient numerical process, based on the combination of time stepping method and meshless local weak formulation, is performed to solve the model. Firstly, an implicit finite difference scheme is used to discrete the problem in time direction. The unconditional stability of the proposed time discretization scheme is proven. Then, a meshfree method based on the combination of local Petrov-Galerkin formulation and strong form is implemented to fully discretize the underlying problem. In our implementation, the radial point interpolation basis functions and local Heaviside step functions are used as the basis and test functions, respectively. A simple collocation process is employed to impose the Dirichlet boundary conditions directly. Finally, two numerical experiments on regular and irregular domains are presented to verify the efficiency, validity and accuracy of the technique.

show abstract

“…In recent years, several algorithms have been proposed for solving boundary value problems by means of radial basis functions [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. Fasshauer [1] has shown that many of the standard algorithms and strategies used for solving ordinary and partial differential equations with polynomial pseudospectral methods can be easily adapted for the use with radial basis functions.…”

Section: Introductionmentioning

confidence: 99%

Imposing various boundary conditions on positive definite kernels

Azarnavid

Nabati

Emamjome

et al. 2019

Applied Mathematics and Computation

View full text Add to dashboard Cite

This paper presents a new approach for the imposing various boundary conditions on radial basis functions and their application in pseudospectral radial basis function method. The various boundary conditions such as Dirichlet, Neumann, Robin, mixed and multi-point boundary conditions, have been considered. Here we propose a new technique to force the radial basis functions to satisfy the boundary conditions exactly. It can improve the applications of existing methods based on radial basis functions especially the pseudospectral radial basis function method to handling the differential equations with more complicated boundary conditions. Several examples of one, two, and three dimensional problems with various boundary conditions have been considered to show the efficacy and versatility of the proposed method.

show abstract

A meshfree method based on the radial basis functions for solution of two-dimensional fractional evolution equation

Cited by 33 publications

References 64 publications

The method of approximate particular solutions to simulate an anomalous mobile‐immobile transport process

The method of approximate particular solutions to simulate an anomalous mobile‐immobile transport process

Application of meshless local Petrov–Galerkin technique to simulate two-dimensional time-fractional Tricomi-type problem

Imposing various boundary conditions on positive definite kernels

Contact Info

Product

Resources

About