On the solution of nonlinear two-point boundary value problems on successively refined grids
type: Item
instance of: scholarly article
title: On the solution of nonlinear two-point boundary value problems on successively refined grids
zbMATH Open document ID: 0619.65074
DOI: 10.1016/0168-9274(85)90032-7
author: Mitchell D. Smooke
author: R. M. M. Mattheij
published in: Applied Numerical Mathematics
publication date: 1985-01-01T00:00:00Z
review text: The solution of nonlinear two-point boundary value problems by adaptive finite difference methods ordinarily proceeds from a coarse to a fine grid. Grid points are inserted in regions of high spatial activity and the coarse grid solution is then interpolated onto the finer mesh. The resulting nonlinear difference equations are often solved by Newton's method. As the size of the mesh spacing becomes small enough, Newton's method converges with only a few iterations. In this paper we derive an estimate that enables us to determine the size of the critical mesh spacing that assures us that the interpolated solution for a class of two-point boundary value problems will lie in the domain of convergence of Newton's method on the next finer grid. We apply the estimate in the solution of several model problems.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 4005497
zbMATH Keywords: mesh refinement
zbMATH Keywords: mildly nonuniform grid
zbMATH Keywords: adaptive finite difference methods
zbMATH Keywords: Newton's method
zbMATH Keywords: convergence
zbMATH Keywords: model problems
describes a project that uses: COLSYS
MaRDI profile type: Publication
full work available at URL: 0168-9274(85)90032-7
OpenAlex ID: W2061345018
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description: scientific article; zbMATH DE number 4005497