SPLINE FUNCTION METHODS FOR NONLINEAR BOUNDARY-VALUE PROBLEMS

被引：13

作者：

BLUE, JL

机构：

[1] Bell Telephone Labs, Inc., Murray Hill, NJ

来源：

COMMUNICATIONS OF THE ACM | 1969年 / 12卷 / 06期

关键词：

boundary value problems; differential equations; finite differences; functional approximation; iterative methods; non-linear equations; spline functions;

D O I：

10.1145/363011.363151

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

The solution of the nonlinear differential equation Y = F(x, Y, Y) with two-point boundary conditions is approximated by a quintic or cubic spline function y(x). The method is well suited to nonuniform mesh size and dynamic mesh size allocation. For uniform mesh size h, the error in the quintic spline y(x) is O(h4), with typical error one-third that from Numerov's method. Requiring the differential equation to be satisfied at the mesh points results in a set of difference equations, which are block tridiagonal and so are easily solved by relaxation or other standard methods. © 1969, ACM. All rights reserved.

引用

页码：327 / &