Tao Hu1, Cheng Huang2, Sergiy Reutskiy3,*, Jun Lu4, Ji Lin5,*
CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.2, pp. 1521-1548, 2024, DOI:10.32604/cmes.2023.030449
Abstract A novel accurate method is proposed to solve a broad variety of linear and nonlinear (1+1)-dimensional and (2+1)-
dimensional multi-term time-fractional partial differential equations with spatial operators of anisotropic diffusivity. For (1+1)-dimensional problems, analytical solutions that satisfy the boundary requirements are derived.
Such solutions are numerically calculated using the trigonometric basis approximation for (2+1)-dimensional
problems. With the aid of these analytical or numerical approximations, the original problems can be converted
into the fractional ordinary differential equations, and solutions to the fractional ordinary differential equations
are approximated by modified radial basis functions with time-dependent coefficients. An efficient backward
substitution strategy that… More >
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