A Sixth-order Tridiagonal Finite Difference Method for General Non-linear Two-point Boundary Value Problems
A Sixth-order Tridiagonal Finite Difference Method for General Non-linear Two-point Boundary Value Problems
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一般非线性两点边值问题的六阶三对角有限差分法
DOI：
10.1093/imamat/24.1.35
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发表时间：
1979
影响因子：
1.2
通讯作者：
M. Chawla
中科院分区：
文献类型：
--
作者：
M. Chawla
本文对一般二阶非线性微分方程Y”=f（x，y，y '），在边界条件y（a）= A，y（B）= B下，给出了一个六阶差分格式.在线性微分方程的情况下，我们的有限差分格式导致三对角线性系统。在适当的条件下，我们证明了有限差分格式的O（h6）-收敛性.数值例子说明了该方法及其六阶收敛性。
We present a sixth-order finite difference method for the general second-order non-linear differential equationY“=f(x, y, y')subject to the boundary conditionsy(a) = A, y(b) = B. In the case of linear differential equations, our finite difference scheme leads to tridiagonal linear systems. We establish, under appropriate conditions,O(h6)-convergence of the finite difference scheme. Numerical examples are given to illustrate the method and its sixth-order convergence.