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

DOI10.1016/j.camwa.2006.03.013zbMath1134.65356OpenAlexW2058926389MaRDI QIDQ2475874

Martin Stynes, Natalia Kopteva

Publication date: 11 March 2008

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2006.03.013

zbMATH Keywords

singular perturbationfinite difference methodnumerical examplesmultiple solutionsboundary layerlayer-adapted meshinterior transition layersemilinear reaction-diffusion two-point boundary value problems

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) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (8)

A class of difference schemes uniformly convergent on a modified Bakhvalov mesh ⋮ Robust adaptive computation of a one-dimensional \(\mathbb Q\)-tensor model of nematic liquid crystals ⋮ Parameter-uniform numerical method for a two-dimensional singularly perturbed convection-reaction-diffusion problem with interior and boundary layers ⋮ A numerical scheme for semilinear singularly perturbed reaction-diffusion problems ⋮ Unnamed Item ⋮ A review on singularly perturbed differential equations with turning points and interior layers ⋮ Analysis of an almost fourth-order parameter-uniformly convergent numerical method for singularly perturbed semilinear reaction-diffusion system with non-smooth source term ⋮ Enriched numerical scheme for singularly perturbed barotropic quasi-geostrophic equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem
• Semilinear elliptic boundary value problems with small parameters
• Singular perturbation methods for ordinary differential equations
• Boundary and interior transition layer phenomena for pairs of second- order differential equations
• Numerical analysis of a singularly perturbed nonlinear reaction-diffusion problem with multiple solutions
• Boundary-interior layer interactions in nonlinear singular perturbation theory
• A uniformly convergent method for a singularly perturbed semilinear reaction–diffusion problem with multiple solutions

This page was built for publication: Numerical analysis of singularly perturbed nonlinear reaction-diffusion problems with multiple solutions