Compact scheme for fractional diffusion-wave equation with spatial variable coefficient and delays. Issue 6 (13th April 2022)

• Record Type: Journal Article
• Authors: Zhang, Qifeng; Liu, Lingling; Zhang, Chengjian
• Is Part Of: Applicable analysis. Volume 101:Issue 6(2022)
• Page Start: 1911
• Page End: 1932
• Publication Date: 2022-04-13
• Subjects: Fractional wave equation with delays -- spatial variable coefficient -- exponential transformation -- maximum error estimate -- numerical stability; 65M06 -- 65M12; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2020.1789600
• Languages: English
• ISSNs: 0003-6811

Abstract

ABSTRACT: In this paper, we study the spatial variable coefficient fractional convection–diffusion wave equation with the singe delay and multi-delay numerically when the exact solution satisfies a certain regularity. First, via the well-known exponential transformation, the delay problem can be greatly simplified, which allows us to use the variable coefficient four-order compact operator. Next, the numerical scheme is derived based on the compact operator and the reduction order method, followed by a linearized technique. Convergence of the full discrete numerical scheme is obtained with convergence order O ( τ 3 − α + h 4 ) under the maximum norm by the energy argument. We prove the almost unconditional stability of the scheme under very mild conditions. Extending the numerical method to the multi-delay case is available. Extensive computational results are presented including single delay and double delay problems, which demonstrate the effectiveness and correctness of the developed schemes.