二维泊松方程基于离散正弦变换的高阶紧致差分方法

A High-order Compact Finite Difference Method Based on Discrete Sine Transform for the 2D Poisson Equation

为了求解带有Dirichlet边界条件的二维泊松方程边值问题,提出了基于快速离散正弦变换的8阶精度的紧致差分格式。引入和推导了8阶精度的紧致差分格式,利用8阶紧致差分格式对泊松方程进行了离散,利用快速离散正弦方法求解离散后的线性系统。通过数值算例验证了该算法的精确性和有效性。

In order to solve the two-dimensional Poisson equation with Dirichlet boundary conditions,an eighth-order accurate compact difference scheme based on fast discrete sinusoidal transform is proposed.The eighth order compact difference scheme is introduced and derived.The Poisson equation is discretized by the eighth order compact difference scheme,and the discrete linear system is solved by the fast discrete sinusoidal method.The accuracy and effectiveness of the algorithm are verified by numerical examples.