## Stability and convergence of the Crank-Nicolson scheme for a class of variable-coefficient tempered fractional diffusion equations.(English)Zbl 1422.65180

Summary: A Crank-Nicolson scheme catering to solving initial-boundary value problems of a class of variable-coefficient tempered fractional diffusion equations is proposed. It is shown through theoretical analysis that the scheme is unconditionally stable and the convergence rate with respect to the space and time step is $$\mathcal{O}(h^{2} +\tau^{2})$$ under a certain condition. Numerical experiments are provided to verify the effectiveness and accuracy of the scheme.

### 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 26A33 Fractional derivatives and integrals 65T50 Numerical methods for discrete and fast Fourier transforms

TFPDE
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