Uniform convergence of a weighted average scheme for a nonlinear reaction-diffusion problem

DOI10.1016/j.cam.2006.01.026zbMath1123.65094OpenAlexW2144751347MaRDI QIDQ869508

Matthew Hardy, Igor P. Boglaev

Publication date: 8 March 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.2006.01.026

zbMATH Keywords

uniform convergencenumerical exampleserror boundsboundary layersCrank-Nicolson methodnonlinear reaction-diffusion equationweighted average difference scheme

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items (9)

Uniform quadratic convergence of monotone iterates for nonlinear singularly perturbed parabolic problems ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ A high order HODIE finite difference scheme for 1D parabolic singularly perturbed reaction-diffusion problems ⋮ Monotone iterates with quadratic convergence rate for solving weighted average approximations to semilinear parabolic problems ⋮ A higher order uniformly convergent method with Richardson extrapolation in time for singularly perturbed reaction-diffusion parabolic problems ⋮ A uniform monotone alternating direction scheme for nonlinear singularly perturbed parabolic problems ⋮ Uniform convergent monotone iterates for semilinear singularly perturbed parabolic problems ⋮ On modified accelerated monotone iterates for solving semilinear parabolic problems ⋮ Robust monotone iterates for nonlinear singularly perturbed boundary value problems

Cites Work

• Finite difference domain decomposition algorithms for a parabolic problem with boundary layers
• On the uniform in small parameter convergence of a weighted scheme for the one-dimensional time-dependent convection-diffusion equation.
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• A monotone weighted average method for a non-linear reaction–diffusion problem
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