Abstract
AbstractIn this article, a two‐step discretization method based on multi‐quadrics (MQ) radial basis function (RBF) is presented for solving Allen–Cahn (AC) equation with integer derivative for time and space. In the first step, backward Euler formula with Newton iterative method is used to discrete the time direction of AC equation. And RBF method is applied in space for solving semi‐discrete linearized problem on a coarse mesh. In the second step, finite difference (FD) and radial basis function‐finite difference (RBF‐FD) methods are used to solve the problem on a fine mesh, respectively. Numerical tests for the equation are obtained to verify the feasibility and computational efficiency of the considered process. In addition, the comparison between FD and RBF‐FD shows that solutions obtained by RBF‐FD are higher accuracy.
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