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The dual reciprocity boundary integral equation technique to solve a class of the linear and nonlinear fractional partial differential equations
Authors:
Mehdi Dehghan
Mansour Safarpoor
Institution:
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran
Abstract:
In this paper, we apply the boundary integral equation technique and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of linear and nonlinear time‐fractional partial differential equations (TFPDEs). The main aim of the present paper is to examine the applicability and efficiency of DRBEM for solving TFPDEs. We employ the time‐stepping scheme to approximate the time derivative, and the method of linear radial basis functions is also used in the DRBEM technique. This method is improved by using a predictor–corrector scheme to overcome the nonlinearity that appears in the nonlinear problems under consideration. To confirm the accuracy of the new approach, several examples are presented. The convergence of the DRBEM is studied numerically by comparing the exact solutions of the problems under investigation. Copyright © 2015 John Wiley & Sons, Ltd.
Keywords:
time‐fractional partial differential equations (TFPDEs)
dual reciprocity boundary elements method (DRBEM)
boundary integral equation method
time‐fractional Fokker–
Planck equations
time‐fractional telegraph equation
time‐fractional sine‐Gordon equations
time‐fractional Klein–
Gordon equations
radial basis functions (RBFs)
boundary elements method (BEM)
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