Space–time spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains

Fakhar-Izadi, Farhad; Dehghan, Mehdi

doi:10.1016/j.camwa.2014.03.016

Cited by 40 publications

(11 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The SEM is developed by Patera as the finite element method combined with spectral technique . The SEM has been applied for several problems such as weakly singular parabolic partial integro‐differential equations, second‐order nonlinear partial differential equations, and mathematical finance for price European options with one asset and stochastic volatility . Also, the interested readers can find more details for SEM in Pozrikidis and Rnquist and Patera .…”

Section: Error Estimate For the Time‐discrete Schemementioning

confidence: 99%

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

Dehghan

Abbaszadeh

2018

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

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 ( 3− ) where 1 < < 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 3476

show abstract

Section: Error Estimate For the Time‐discrete Schemementioning

confidence: 99%

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

Dehghan

Abbaszadeh

2018

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…A numerical solution of weakly singular integral equation was also discussed in [2,11]. Also see [1,7,13,21,22].…”

Section: Introductionmentioning

confidence: 97%

Tau approximate solution of weakly singular Volterra integral equations with Legendre wavelet basis

Pourgholi

Tahmasebi

Azimi

2016

International Journal of Computer Mathematics

View full text Add to dashboard Cite

In this paper, a spectral Tau method based on Legendre Wavelet basis is proposed. For this purpose we present a stable operational Tau method based on Legendre Wavelet basis. This method provides an efficient approximate solution for weakly singular Volterra integral equations by using reduced set of matrix operations. An error estimation of the Tau method is also introduced. Finally we demonstrate the validity and applicability of the method by numerical examples. ARTICLE HISTORY

show abstract

“…Due to the ill‐conditioning of the resultant linear systems in global RBF‐collocation method and in order to avoiding computational cost of numerical integration scheme in meshless methods based on weak forms, various approaches are proposed to evade this problem, Refs. being among them, and the latest one, so‐called spectral meshless radial point interpolation (SMRPI) method, has been proposed in .…”

Section: Introductionmentioning

confidence: 99%

Stability and convergence of spectral radial point interpolation method locally applied on two‐dimensional pseudoparabolic equation

Shivanian

Aslefallah

2016

Numerical Methods Partial

View full text Add to dashboard Cite

In this article, we study a spectral meshless radial point interpolation of pseudoparabolic equations in two spatial dimensions. Shape functions, which are constructed through point interpolation method using the radial basis functions, help us to treat problem locally with the aim of high‐order convergence rate. The time derivatives are approximated by the finite difference time‐stepping method. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical results are presented to illustrate the theoretical findings. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 724–741, 2017

show abstract

Space–time spectral method for a weakly singular parabolic partial integro-differential equation on irregular domains

Cited by 40 publications

References 51 publications

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

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

Tau approximate solution of weakly singular Volterra integral equations with Legendre wavelet basis

Stability and convergence of spectral radial point interpolation method locally applied on two‐dimensional pseudoparabolic equation

Contact Info

Product

Resources

About