Numerical Analysis of a 2d Singularly Perturbed Semilinear Reaction-Diffusion Problem

DOI10.1007/978-3-642-00464-3_8zbMath1233.65081OpenAlexW1800410760MaRDI QIDQ3615644

Natalia Kopteva

Publication date: 24 March 2009

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-00464-3_8

zbMATH Keywords

second-order convergencelayer-adapted meshestwo-dimensional domainsemilinear reaction-diffusion equationdiffusion parameterdiscrete maximum normmaximum norm error analysisnumber of mesh nodesordered set of boundary points

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Error bounds for boundary value problems involving PDEs (65N15) Finite difference methods for boundary value problems involving PDEs (65N06) Semilinear elliptic equations (35J61)

Related Items (7)

Internal layers in the one-dimensional reaction-diffusion equation with a discontinuous reactive term ⋮ Numerical simulation of front dynamics in a nonlinear singularly perturbed reaction-diffusion problem ⋮ On Extension of Asymptotic Comparison Principle for Time Periodic Reaction-Diffusion-Advection Systems with Boundary and Internal Layers ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Development of methods of asymptotic analysis of transition layers in reaction-diffusion-advection equations: theory and applications ⋮ Analytical-numerical approach to describing time-periodic motion of fronts in singularly perturbed reaction-advection-diffusion models ⋮ Use of Asymptotics for New Dynamic Adapted Mesh Construction for Periodic Solutions with an Interior Layer of Reaction-Diffusion-Advection Equations

Cites Work

• Semilinear elliptic boundary value problems with small parameters
• Mathematical biology. Vol. 2: Spatial models and biomedical applications.
• Numerical analysis of a singularly perturbed nonlinear reaction-diffusion problem with multiple solutions
• Maximum norm error analysis of a 2d singularly perturbed semilinear reaction-diffusion problem
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