Theoretical Analysis (Convergence and Stability) of a Difference Approximation for Multiterm Time Fractional Convection Diffusion-Wave Equations with Delay

A. S. Hendy and R. H. De Staelen
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A. S. Hendy: Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., 620002 Yekaterinburg, Russia
R. H. De Staelen: Department of Electronics and Information Systems, Ghent University, 9000 Gent, Belgium

Mathematics, 2020, vol. 8, issue 10, 1-20

Abstract: In this paper, we introduce a high order numerical approximation method for convection diffusion wave equations armed with a multiterm time fractional Caputo operator and a nonlinear fixed time delay. A temporal second-order scheme which is behaving linearly is derived and analyzed for the problem under consideration based on a combination of the formula of L 2 − 1 σ and the order reduction technique. By means of the discrete energy method, convergence and stability of the proposed compact difference scheme are estimated unconditionally. A numerical example is provided to illustrate the theoretical results.

Keywords: fractional convection diffusion-wave equations; compact difference scheme; nonlinear delay; spatial variable coefficients; convergence and stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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