Error analysis of fast L1 ADI finite difference/compact difference schemes for the fractional telegraph equation in three dimensions

Leijie Qiao, Wenlin Qiu and Da Xu

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 205, issue C, 205-231

Abstract: This article proposes the fast L1 alternating direction implicit (ADI) finite difference and compact difference schemes to solve the fractional telegraph equation in three-dimensional space. The fully-discrete fast L1 ADI finite difference scheme can be established via the fast L1 formula for the approximation of mixed Caputo fractional derivatives and the central difference formula for the approximation of the spatial derivative term, then from which an ADI algorithm is designed to reduce three-dimensional problems to a series of one-dimensional problems. We add the corresponding compact operators in all directions of the space to get the fully-discrete L1 ADI compact difference scheme. Then the convergence in L2 and H1 norms of two ADI schemes is derived via energy method. Eventually, numerical experiments are carried out to verify the theoretical estimates.

Keywords: Three-dimensional fractional telegraph equation; ADI difference/compact difference methods; Fast L1 algorithm; Convergence analysis; Numerical examples (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:205:y:2023:i:c:p:205-231

DOI: 10.1016/j.matcom.2022.10.001

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