The Rational Spectral Method Combined with the Laplace Transform for Solving the Robin Time-Fractional Equation

• Published in: Advances in Mathematical Physics Vol. 2020; no. 2020; pp. 1 - 7
• Main Author: Yang, Lufeng
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 2020; Hindawi; John Wiley & Sons, Inc; Wiley
• Subjects: Algorithms; Analysis; Boundary conditions; Calculus; Differential equations; Laplace transforms; Linear equations; Mathematical functions; Methods; Navier-Stokes equations; Numerical analysis; Ordinary differential equations; Partial differential equations; Spectra; Spectral methods
• ISSN: 1687-9120; 1687-9139
• DOI: 10.1155/2020/9865682

In this paper, the rational spectral method combined with the Laplace transform is proposed for solving Robin time-fractional partial differential equations. First, a time-fractional partial differential equation is transformed into an ordinary differential equation with frequency domain components by the Laplace transform. Then, the spatial derivatives are discretized by the rational spectral method, the linear equation with the parameter s is solved, and the approximation Ux,s is obtained. The approximate solution at any given time, which is the numerical inverse Laplace transform, is obtained by the modified Talbot algorithm. Numerical experiments are carried out to demonstrate the high accuracy and efficiency of our method.