Operator splitting scheme based on barycentric Lagrange interpolation collocation method for the Allen-Cahn equation

In this paper, we consider the operator splitting scheme based on barycentric Lagrange interpolation collocation method for the two-dimensional Allen-Cahn equation. The original problem is split into linear and nonlinear subproblems: the linear part is solved by barycentric Lagrange interpolation collocation method in space and Crank-Nicolson scheme in time; the nonlinear part is solved analytically due to the availability of a closed-form solution. The error estimates of the proposed scheme are studied. Numerical experiments are carried out to demonstrate the accuracy and efficiency of the two operator splitting schemes.