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Rational spline-nonstandard finite difference scheme for the solution of time-fractional Swift-Hohenberg equation. (English) Zbl 1429.65205
Summary: 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.
MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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