Rational spline-nonstandard finite difference scheme for the solution of time-fractional Swift–Hohenberg equation

摘要

In this paper, we introduce a new scheme based on rational spline function and nonstandard finite difference technique to solve the time-fractional Swift–Hohenberg equation in the sense of Riemann–Liouville derivative. Via Fourier method, the method is convergent and unconditionally stable. Also, we investigated the existence and uniqueness of the proposed method. Numerical results are demonstrated to validate the applicability and the theoretical results.