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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.
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
Full Text: DOI
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