非线性常微分方程边值问题的三次样条解

摘要

对一类线性(非线性)常微分方程边值问题,以Legendre-Gauss-Lobatto节点为配置点,利用含参数的三次样条函数求其数值解.根据方程不同类型的边界条件,构造其算法格式,选取适当的参数值,以提高数值误差的精度.本算法格式构造简单,数值结果验证了算法的有效性和高精度.%Based on Legendre-Gauss-Lobatto nodes,the numerical solution of boundary value problems of linear (nonlinear) ordinary differential equations is investigated by using parametric cubic spline function.Regarding different boundary conditions,the algorithm scheme of equations is structured respectively and parameters are appropriately chosen to improve accuracy.The algorithms are easy to implement.Numerical results demonstrate the efficiency and accuracy of the proposed algorithms.