Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran
Abstract
In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integration by using initial condi\-tions. This leads to fewer computations rather than the standard FIM. Also, a product Simpson method is used to overcome the singularity included in the definition of fractional derivatives, and an integration matrix is obtained. Some numerical examples are provided to show the efficiency of the method. In addition, a comparison is made between the proposed method and the previous ones.
Biazar, J., & Asadi, M. A. (2019). Finite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients. Computational Methods for Differential Equations, 7(1), 1-15.
MLA
Jafar Biazar; Mohammad Ali Asadi. "Finite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients". Computational Methods for Differential Equations, 7, 1, 2019, 1-15.
HARVARD
Biazar, J., Asadi, M. A. (2019). 'Finite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients', Computational Methods for Differential Equations, 7(1), pp. 1-15.
VANCOUVER
Biazar, J., Asadi, M. A. Finite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients. Computational Methods for Differential Equations, 2019; 7(1): 1-15.
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