An Efficient Numerical Method for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations

DOI10.1007/978-3-642-18466-6_58zbMath1318.65055OpenAlexW1868729350MaRDI QIDQ3075300

Sunil Kumar, S. Chandra Sekhara Rao

Publication date: 11 February 2011

Published in: Numerical Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-18466-6_58

zbMATH Keywords

Shishkin meshsingularly perturbedparameter-uniform convergencesystem of semilinear equations

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Semilinear parabolic equations (35K58)

Related Items (5)

Higher order computational method for a singularly perturbed nonlinear system of differential equations ⋮ Unnamed Item ⋮ Parameter-uniform convergence of a numerical method for a coupled system of singularly perturbed semilinear reaction-diffusion equations with boundary and interior layers ⋮ Analysis and implementation of a computational technique for a coupled system of two singularly perturbed parabolic semilinear reaction-diffusion equations having discontinuous source terms ⋮ Analysis of an almost fourth-order parameter-uniformly convergent numerical method for singularly perturbed semilinear reaction-diffusion system with non-smooth source term

Cites Work

• A singularly perturbed semilinear system
• Singularly perturbed phenomena of semilinear second order systems
• Uniform fourth order difference scheme for a singular perturbation problem
• On diagonal dominance arguments for bounding \(\| A^{-1}\|_\infty\)
• A uniformly accurate spline collocation method for a normalized flux.
• Nonlinear singular perturbation phenomena: theory and applications
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• A System of Singularly Perturbed Semilinear Equations
• CONSERVATIVE NUMERICAL METHOD FOR A SYSTEM OF SEMILINEAR SINGULARLY PERTURBED PARABOLIC REACTION‐DIFFUSION EQUATIONS
• The necessity of Shishkin decompositions

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