## A second order BDF alternating direction implicit difference scheme for the two-dimensional fractional evolution equation.(English)Zbl 1443.65439

Summary: A second order backward differentiation formula (BDF) alternating direction implicit (ADI) difference scheme is formulated and analyzed for the two-dimensional fractional evolution equation. In this method, standard central difference approximation used for the spatial discretization and the time stepping – an alternating direction implicit scheme based on second order convolution quadrature suggested by Lubich and second order BDF are considered. The stability and convergence of the second order BDF ADI difference scheme in $$L_2$$ norm are derived by the energy method. Numerical experiments in total agreement with our analysis are reported.

### MSC:

 65R20 Numerical methods for integral equations 45K05 Integro-partial differential equations 26A33 Fractional derivatives and integrals 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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