Laplace方程的三次样条函数数值解法

Numerical Solutions for Laplace Equation Using Cubic Splines

本文采用三次样条函数方法对 Laplace 方程以样条——Seidel 方法,样条——松驰法和样条——时间相关法求解.各种方法均分别采用样条2,样条4而得到 Laplace 方程的数值解,并与有限差分法及精确解进行比较,计算精度是令人满意的.

In this paper,a cubic spline is used for the solution of Laplaceequation by Spline-Seidel method,Spline-relaxation and Spline-time-depen-dent method.Numerical solutions of Laplace equation have been obtainedwith Spline 9 and Spline 4.Comparison between exact solutions or theresults obtained from finite difference is provided.