Improved finite difference method with a compact correction term for solving Poisson's equations

摘要

An improved finite difference method with a compact correction term is proposed to solve the Poisson's equations. The compact correction term is developed by coupled high-order compact and low-order classical finite difference formulations. The numerical solutions obtained by the classical finite difference method are considered as fundamental solutions with lower accuracy, whereas a compact correction term is added into the source term of classical discrete formulation to improve the accuracy of numerical solutions. The proposed method can be extended from two-dimensional to multidimensional cases straightforwardly. Numerical experiments are carried out to verify the accuracy and efficiency of this method.