Improved Finite Difference Method with a Compact Correction Term for Solving Poisson's Equations
For computational scientists solving Poisson equations, this method offers a straightforward way to improve accuracy without significantly increasing complexity.
The paper proposes an improved finite difference method with a compact correction term for solving Poisson equations, achieving higher accuracy than classical finite difference methods. Numerical experiments verify the method's accuracy and efficiency.
An improved finite difference method with compact correction term is proposed to solve the Poisson equations. The compact correction term is developed by a 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 compact correction term is added into source term of classical discrete formulation to improve the accuracy of numerical solutions. The proposed method can be extended from two- to multi-dimensional cases straightforwardly. Numerical experiments are carried out to verify the accuracy and efficiency of this method.