A Legendre spectral element method (SEM) based on the modified bases for solving neutral delay distributed-order fractional damped diffusion-wave equation

作者：Dehghan, Mehdi^*; Abbaszadeh, Mostafa

来源：Mathematical Methods in the Applied Sciences, 2018, 41(9): 3476-3494.

DOI：10.1002/mma.4839

• 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

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 O(tau(3-mu)) where 1 < alpha < 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.

• 出版日期2018-6