A fast adaptive numerical method for stiff two-point boundary value problems

June Yub Lee, Leslie Greengard

Research output: Contribution to journalArticle

Abstract

We describe a robust, adaptive algorithm for the solution of singularly perturbed two-point boundary value problems. Many different phenomena can arise in such problems, including boundary layers, dense oscillations, and complicated or ill-conditioned internal transition regions. Working with an integral equation reformulation of the original differential equation, we introduce a method for error analysis which can be used for mesh refinement even when the solution computed on the current mesh is underresolved. Based on this method, we have constructed a black-box code for stiff problems which automatically generates an adaptive mesh resolving all features of the solution. The solver is direct and of arbitrarily high-order accuracy and requires an amount of time proportional to the number of grid points.

Original languageEnglish (US)
Pages (from-to)403-429
Number of pages27
JournalSIAM Journal on Scientific Computing
Volume18
Issue number2
StatePublished - Mar 1997

Fingerprint

Adaptive Method
Two-point Boundary Value Problem
Boundary value problems
Numerical methods
Numerical Methods
Stiff Problems
High Order Accuracy
Singularly Perturbed Boundary Value Problem
Adaptive Mesh
Mesh Refinement
Black Box
Adaptive Algorithm
Reformulation
Error Analysis
Boundary Layer
Integral Equations
Directly proportional
Mesh
Oscillation
Differential equation

Keywords

  • Integral equations
  • Mesh refinement
  • Singular perturbations problems

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

A fast adaptive numerical method for stiff two-point boundary value problems. / Lee, June Yub; Greengard, Leslie.

In: SIAM Journal on Scientific Computing, Vol. 18, No. 2, 03.1997, p. 403-429.

Research output: Contribution to journalArticle

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