Numerical analysis of a singularly perturbed nonlinear reaction-diffusion problem with multiple solutions

DOI10.1016/j.apnum.2004.07.001zbMath1069.65087OpenAlexW1996672882MaRDI QIDQ1886268

Martin Stynes, Natalia Kopteva

Publication date: 18 November 2004

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2004.07.001

zbMATH Keywords

numerical resultssingular perturbationerror estimatesdynamical systemsBakhvalov meshShishkin meshlayer-adapted meshnonlinear reaction-diffusion equationsub-solutionssuper-solutions

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular perturbations for ordinary differential equations (34E15) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

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Cites Work

• Semilinear elliptic boundary value problems with small parameters
• Uniform fourth order difference scheme for a singular perturbation problem
• Singular perturbation methods for ordinary differential equations
• Slowly Varying Phase Planes and Boundary-Layer Theory
• Boundary-interior layer interactions in nonlinear singular perturbation theory
• A uniformly convergent method for a singularly perturbed semilinear reaction–diffusion problem with multiple solutions
• Uniform pointwise convergence of difference schemes for convection-diffusion problems on layer-adapted meshes
• Sufficient conditions for uniform convergence on layer-adapted grids
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