A Runge–Kutta Gegenbauer spectral method for nonlinear fractional differential equations with Riesz fractional derivatives. Issue 2 (1st February 2019)

• Record Type: Journal Article
• Authors: Lin, Fu-Rong; Qu, Haidong
• Is Part Of: International journal of computer mathematics. Volume 96:Issue 2(2019)
• Page Start: 417
• Page End: 435
• Publication Date: 2019-02-01
• Subjects: Fractional differential equation -- Riemann–Liouville fractional derivative -- Riesz fractional derivative -- Runge–Kutta method -- shifted Gegenbauer polynomial; 35R11 -- 26A33 -- 65R10 -- 78M22; Computers -- Periodicals; Numerical analysis -- Periodicals; Automation -- Periodicals; 004.0151
• DOI: 10.1080/00207160.2018.1487059
• Languages: English
• ISSNs: 0020-7160

Abstract

ABSTRACT: A Runge–Kutta Gegenbauer spectral method is proposed to solve an initial-boundary value problem for a nonlinear two-dimensional fractional differential equation with variable coefficients. The solution to the problem at each time step is approximated by a bivariate polynomial based on shifted Gegenbauer polynomials and then the Runge–Kutta method of order 3 is applied to the problem. The convergence rate of the derived method is analysed. Numerical results are presented to verify the effectiveness of the method.