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 language | English (US) |
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Pages (from-to) | 403-429 |
Number of pages | 27 |
Journal | SIAM Journal on Scientific Computing |
Volume | 18 |
Issue number | 2 |
DOIs | |
State | Published - Mar 1997 |
Keywords
- Integral equations
- Mesh refinement
- Singular perturbations problems
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics