The layer-resolving transformation and mesh generation for quasilinear singular perturbation problems

Authors:
Relja Vulanović
Affiliations:
Department of Mathematical Sciences, Kent State University Stark Campus, 6000 Frank Ave. NW, Canton, OH 44720-7599, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

Citing 6
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Sufficient conditions for uniform convergence on layer-adapted grids

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Abstract

The relationship is analyzed between layer-resolving transformations and mesh-generating functions for numerical solution of singularly perturbed boundary-value problems. The analysis is carried out for one-dimensional quasilinear problems without turning points, which are discretized by first-order finite-difference schemes. It is proved that if a general layer-resolving function is used to generate the discretization mesh, then the numerical solution converges uniformly in the perturbation parameter.