Preconditioned Pseudo-Spectral Gradient Flow for Computing the Steady-State of Space Fractional Cahn-Allen Equations With Variable Coefficients

Abstract

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The aim of this paper is to propose some efficient and accurate numerical methods to compute the steady-state of variable coefficients space fractional Cahn-Allen equations. The approach combines an adaptive time stepping semi-implicit gradient flow method to minimize the fractional energy functional and pseudo-spectral approximation schemes. Based on the use of a preconditioned GMRES, the space fractional Cahn-Allen equation is then solved efficiently. The full methodology is supported by the numerical solution of a one-dimensional problem.

Keywords

• nonlinear pseudodifferential equation
• fractional derivative
• dynamics
• gradient flow
• pseudo-spectral method