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.
Acknowledgments
The authors would like to thank the referees for their valuable comments and suggestions which improve the quality of the paper.
Disclosure statement
No potential conflict of interest was reported by the authors.