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A Legendre spectral element method (SEM) based on the modified bases for solving neutral delay distributed‐order fractional damped diffusion‐wave equation
Abstract:The main purpose of the current paper is to propose a new numerical scheme based on the spectral element procedure for simulating the neutral delay distributed‐order fractional damped diffusion‐wave equation. To this end, the temporal direction has been discretized by a finite difference formula with convergence order urn:x-wiley:mma:media:mma4839:mma4839-math-0001 where 1<α<2. In the next, to obtain a full‐discrete scheme, we apply the spectral finite element method on the spatial direction. Furthermore, the unconditional stability of semidiscrete scheme and convergence order of full‐discrete scheme of new technique are discussed. Finally, 2 test problems have been considered to demonstrate the ability and efficiency of the proposed numerical technique.
Keywords:spectral element method  fractional delay PDE  finite difference scheme and energy method  stability and convergence analysis  distributed‐order fractional equation  fractional damped diffusion‐wave equation
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