The dual reciprocity boundary elements method for the linear and nonlinear two-dimensional time-fractional partial differential equations

摘要

In this paper, we apply the dual reciprocity boundary elements method for the numerical solution of two-dimensional linear and nonlinear time-fractional modified anomalous subdiffusion equations and time-fractional convection-diffusion equation. The fractional derivative of problems is described in the Riemann-Liouville and Caputo senses. We employ the linear radial basis function for interpolation of the nonlinear, inhomogeneous and time derivative terms. This method is improved by using a predictor-corrector scheme to overcome the nonlinearity which appears in the nonlinear problems under consideration. The accuracy and efficiency of the proposed schemes are checked by five test problems. The proposed method is employed for solving some examples in two dimensions on unit square and also in complex regions to demonstrate the efficiency of the new technique. Copyright (C) 2016 John Wiley & Sons, Ltd.