Numerical methods for evolutionary reaction-diffusion problems with nonlinear reaction terms.

DOI10.1016/j.cam.2003.09.030zbMath1051.65089OpenAlexW2007858318MaRDI QIDQ1428496

B. Bujanda, J. C. Jorge

Publication date: 29 March 2004

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.2003.09.030

zbMATH Keywords

algorithmscomputational complexityconvergenceShishkin meshesfractional step methodsnonlinear reaction-diffusion equationadditive Runge-Kutta methodsalternating direction methodsnonlinear stiff problems

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Complexity and performance of numerical algorithms (65Y20)

Related Items (7)

The convergence and stability of splitting finite-difference schemes for nonlinear evolutionary equations ⋮ A robust numerical scheme for singularly perturbed parabolic reaction-diffusion problems via the method of lines ⋮ A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Parameter uniform numerical scheme for time dependent singularly perturbed convection-diffusion-reaction problems with general shift arguments ⋮ Stability results for linearly implicit fractional step discretizations of nonlinear time dependent parabolic problems ⋮ Mathematics and wine

Cites Work

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• The Numerical Solution of Parabolic and Elliptic Differential Equations
• Additive Methods for the Numerical Solution of Ordinary Differential Equations
• On the non-existence of 𝜀-uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems
• An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems
• A Uniformly Convergent Finite Difference Scheme for a Singularly Perturbed Semilinear Equation
• Stability results for fractional step discretizations of time dependent coefficient evolutionary problems

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