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A new high order ADI numerical difference formula for time-fractional convection-diffusion equation. (English) Zbl 1474.35675

Summary: Based on exponential transformation, quadratic interpolation polynomial and Padé approximation, a new high order finite difference scheme is proposed for solving the two-dimensional (2D) time-fractional convection-dominated diffusion equation (of order \(\alpha \in (0, 1))\). The resulting scheme is of \((3 - \alpha)\)-order accuracy in time and fourth-order accuracy in space. In order to reduce the amount of computation, the alternating direction implicit (ADI) scheme is further developed. Numerical experiments are given to demonstrate the high accuracy and robustness of our new scheme.

MSC:

35R11 Fractional partial differential equations
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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