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

DOI10.1016/j.cam.2006.03.020zbMath1116.65094OpenAlexW2021272693MaRDI QIDQ875167

Relja Vulanović

Publication date: 11 April 2007

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2006.03.020

zbMATH Keywords

numerical resultssingular perturbationuniform convergenceconvection-diffusion equationfinite difference schemeBakhvalov meshmesh generationShishkin meshlayer-resolving transformationquasilinear boundary-value problems

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items

A brief survey on numerical methods for solving singularly perturbed problems ⋮ Numerical treatment of a quasilinear initial value problem with boundary layer

Cites Work

• A uniform numerical method for quasilinear singular perturbation problems without turning points
• Uniform second-order pointwise convergence of a finite difference discretization for a quasilinear problem
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• Application of notions and relations of differential geometry to grid generation
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• Uniform Pointwise Convergence on Shishkin-Type Meshes for Quasi-Linear Convection-Diffusion Problems
• The optimization of methods of solving boundary value problems with a boundary layer
• Sufficient conditions for uniform convergence on layer-adapted grids
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