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The dual reciprocity boundary integral equation technique to solve a class of the linear and nonlinear fractional partial differential equations
Author(s) -
Dehghan Mehdi,
Safarpoor Mansour
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3707
Subject(s) - mathematics , nonlinear system , reciprocity (cultural anthropology) , partial differential equation , convergence (economics) , mathematical analysis , fractional calculus , boundary (topology) , dual (grammatical number) , psychology , social psychology , art , physics , literature , quantum mechanics , economics , economic growth
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.