An efficient reproducing kernel method for solving the Allen-Cahn equation

Abstract In this paper, an efficient reproducing kernel method combined with the finite difference method and the Quasi-Newton method is proposed to solve the Allen–Cahn equation. Based on the Legendre polynomials, we construct a new reproducing kernel function with polynomial form. We prove that the semi-scheme can preserve the energy dissipation property unconditionally. Numerical experiments are given to show the efficiency and validity of the proposed scheme.

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