Orthogonal spline collocation for nonlinear Dirichlet problems

被引：1

作者：

Aitbayev, R ^{[1
]}

Bialecki, B ^{[1
]}

机构：

[1] Colorado Sch Mines, Dept Math & Comp Sci, Golden, CO 80401 USA

来源：

SIAM JOURNAL ON NUMERICAL ANALYSIS | 2000年 / 38卷 / 05期

关键词：

orthogonal spline collocation; Dirichlet problem; nonlinear; existence; uniqueness; error estimates; Newton's method;

D O I：

10.1137/S0036142999354538

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the orthogonal spline collocation ( OSC) solution of a homogeneous Dirichlet boundary value problem in a rectangle for a general nonlinear elliptic partial differential equation. The approximate solution is sought in the space of Hermite bicubic splines. We prove local existence and uniqueness of the OSC solution, obtain optimal order H-1 and H-2 error estimates, and prove the quadratic convergence of Newton's method for solving the OSC problem.

引用

页码：1582 / 1602

页数：21

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