Orthogonal spline collocation for nonlinear Dirichlet problems

Authors
Aitbayev, R Bialecki, B
Citation
R. Aitbayev et B. Bialecki, Orthogonal spline collocation for nonlinear Dirichlet problems, SIAM J NUM, 38(5), 2000, pp. 1582-1602
Citations number
22
Categorie Soggetti
Mathematics
Journal title
SIAM JOURNAL ON NUMERICAL ANALYSIS
ISSN journal
00361429 → ACNP
Volume
38
Issue
5
Year of publication
2000
Pages
1582 - 1602
Database
ISI
SICI code
0036-1429(200012)38:5<1582:OSCFND>2.0.ZU;2-P
Abstract
We study the orthogonal spline collocation ( OSC) solution of a homogeneous Dirichlet boundary value problem in a rectangle for a general nonlinear el liptic partial differential equation. The approximate solution is sought in the space of Hermite bicubic splines. We prove local existence and uniquen ess 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.