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The implicit midpoint method for Riesz tempered fractional diffusion equation with a nonlinear source term. (English) Zbl 1458.65108
Summary: In this paper, the implicit midpoint method is presented for solving Riesz tempered fractional diffusion equation with a nonlinear source term, where the tempered fractional partial derivatives are evaluated by the modified second-order Lubich tempered difference operator. Stability and convergence analyses of the numerical method are given. The numerical experiments demonstrate that the proposed method is effective.
MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
60G51 Processes with independent increments; Lévy processes
35K05 Heat equation
Software:
TFPDE
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