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

A. S. Hendy, R. H. De Staelen
2020 Mathematics  
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 L2−1σ and the order reduction technique. By means of the discrete energy method, convergence and stability of the proposed compact
more » ... ed compact difference scheme are estimated unconditionally. A numerical example is provided to illustrate the theoretical results.
doi:10.3390/math8101696 fatcat:3sigb57s2zgwdn7jzmryci3xki