A new high order ADI numerical difference formula for time-fractional convection-diffusion equation

Longyuan Wu and Shuying Zhai

Applied Mathematics and Computation, 2020, vol. 387, issue C

Abstract: 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 α ∈ (0, 1)). The resulting scheme is of (3−α)-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.

Keywords: Caputo fractional derivative; Time-fractional convection-diffusion equation; Exponential transformation; Padé approximation; ADI method (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:387:y:2020:i:c:s0096300319305478

DOI: 10.1016/j.amc.2019.124564

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