The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-Differential Equation with a Weakly Singular Kernel
Year: 2013
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 3 : pp. 556–570
Abstract
The $z$-transform is introduced to analyze a full discretization method for a partial integro-differential equation (PIDE) with a weakly singular kernel. In this method, spectral collocation is used for the spatial discretization, and, for the time stepping, the finite difference method combined with the convolution quadrature rule is considered. The global stability and convergence properties of complete discretization are derived and numerical experiments are reported.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2013.1111nm
Numerical Mathematics: Theory, Methods and Applications, Vol. 6 (2013), Iss. 3 : pp. 556–570
Published online: 2013-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Partial integro-differential equation weakly singular kernel spectral collocation methods $z$-transform convolution quadrature.
-
Bivariate Chebyshev polynomials of the fifth kind for variable-order time-fractional partial integro-differential equations with weakly singular kernel
Sadri, Khadijeh | Hosseini, Kamyar | Baleanu, Dumitru | Ahmadian, Ali | Salahshour, SoheilAdvances in Difference Equations, Vol. 2021 (2021), Iss. 1
https://doi.org/10.1186/s13662-021-03507-5 [Citations: 14] -
Numerical solutions of viscoelastic bending wave equations with two term time kernels by Runge-Kutta convolution quadrature
Xu, Da
Discrete & Continuous Dynamical Systems - B, Vol. 22 (2017), Iss. 6 P.2389
https://doi.org/10.3934/dcdsb.2017122 [Citations: 0] -
Approximation of partial integro differential equations with a weakly singular kernel using local meshless method
Ali, Gohar | Gómez-Aguilar, J.F.Alexandria Engineering Journal, Vol. 59 (2020), Iss. 4 P.2091
https://doi.org/10.1016/j.aej.2020.01.010 [Citations: 13] -
Second-order difference approximations for Volterra equations with the completely monotonic kernels
Xu, Da
Numerical Algorithms, Vol. 81 (2019), Iss. 3 P.1003
https://doi.org/10.1007/s11075-018-0580-5 [Citations: 5] -
Finite difference schemes for time-fractional Schrödinger equations via fractional linear multistep method
Hicdurmaz, Betul
International Journal of Computer Mathematics, Vol. 98 (2021), Iss. 8 P.1561
https://doi.org/10.1080/00207160.2020.1834088 [Citations: 2] -
High order WSGL difference operators combined with Sinc-Galerkin method for time fractional Schrödinger equation
Yan, Shaodan | Zhao, Fengqun | Li, Can | Zhao, LeInternational Journal of Computer Mathematics, Vol. 97 (2020), Iss. 11 P.2259
https://doi.org/10.1080/00207160.2019.1692200 [Citations: 3] -
An efficient numerical approach for solving variable-order fractional partial integro-differential equations
Wang, Yifei | Huang, Jin | Deng, Ting | Li, HuComputational and Applied Mathematics, Vol. 41 (2022), Iss. 8
https://doi.org/10.1007/s40314-022-02131-7 [Citations: 0] -
Numerical solution of Volterra partial integro-differential equations based on sinc-collocation method
Fahim, Atefeh | Fariborzi Araghi, Mohammad Ali | Rashidinia, Jalil | Jalalvand, MehdiAdvances in Difference Equations, Vol. 2017 (2017), Iss. 1
https://doi.org/10.1186/s13662-017-1416-7 [Citations: 18]