Taiwanese Journal of Mathematics
- Taiwanese J. Math.
- Volume 23, Number 4 (2019), 981-1000.
Spectral Approximations for Nonlinear Fractional Delay Diffusion Equations with Smooth and Nonsmooth Solutions
A fully discrete scheme is proposed for the nonlinear fractional delay diffusion equations with smooth solutions, where the fractional derivative is described in Caputo sense with the order $\alpha$ ($0 \lt \alpha \lt 1$). The scheme is constructed by combining finite difference method in time and Legendre spectral approximation in space. Stability and convergence are proved rigorously. Moreover, a modified scheme is proposed for the equation with nonsmooth solutions by adding correction terms to the approximations of fractional derivative operator and nonlinear term. Numerical examples are carried out to support the theoretical analysis.
Taiwanese J. Math., Volume 23, Number 4 (2019), 981-1000.
Received: 9 February 2018
Revised: 3 September 2018
Accepted: 9 September 2018
First available in Project Euclid: 18 July 2019
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 65M12: Stability and convergence of numerical methods 65M06: Finite difference methods 65M70: Spectral, collocation and related methods 35R11: Fractional partial differential equations
Liu, Haiyu; Lü, Shujuan; Chen, Hu. Spectral Approximations for Nonlinear Fractional Delay Diffusion Equations with Smooth and Nonsmooth Solutions. Taiwanese J. Math. 23 (2019), no. 4, 981--1000. doi:10.11650/tjm/180901. https://projecteuclid.org/euclid.twjm/1563436877