Numerical solution of the general high-dimensional multi-term time-space-fractional diffusion equations
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In this article, an advanced differential quadrature (DQ) approach is proposed to obtain the numerical solutions of the two- and three-dimensional multi-term time-space-fractional diffusion equation (TSFDE) on general domains. The fractional derivatives in space are firstly discretized by deriving a new class of differential quadrature (DQ) formulas with radial basis functions (RBFs) being the trial functions. Then, the original problems are converted to a group of multi-term fractional ordinary differential equations (ODEs), which are further treated by a class of high-order difference schemes based on the weighted and shifted Lubich difference operators. The presented DQ method is high accurate and convergent on arbitrary domains. Finally, several numerical examples are carried out to illustrate its accuracy and effectiveness.
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