Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 39, Issue 10, Pages 2461-2476Publisher
WILEY
DOI: 10.1002/mma.3707
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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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 (c) 2015 John Wiley & Sons, Ltd.
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