High order parameter-robust numerical method for singularly perturbed reaction-diffusion problems

DOI10.1016/j.amc.2010.01.121zbMath1229.65129OpenAlexW2042719590MaRDI QIDQ972144

Mukesh Kumar, S. Chandra Sekhara Rao

Publication date: 25 May 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.01.121

zbMATH Keywords

singular perturbationnumerical examplesglobal error estimatereaction-diffusion problemscentral difference schemehybrid schemefourth-order compact difference schemepointwise error estimateparameter-robust convergencegeneralized Shishkin meshlinear self-adjoint two-point boundary-value problems

Mathematics Subject Classification ID

Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

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High order parameter-uniform discretization for singularly perturbed parabolic partial differential equations with time delay ⋮ A second order numerical method for singularly perturbed problem with non-local boundary condition ⋮ ROBUST NUMERICAL METHOD FOR SINGULARLY PERTURBED CONVECTION-DIFFUSION TYPE PROBLEMS WITH NON-LOCAL BOUNDARY CONDITION ⋮ A modified graded mesh and higher order finite element method for singularly perturbed reaction-diffusion problems ⋮ Exponential fitted operator method for singularly perturbed convection-diffusion type problems with nonlocal boundary condition ⋮ Optimal fourth-order parameter-uniform convergence of a non-monotone scheme on equidistributed meshes for singularly perturbed reaction–diffusion problems ⋮ Parameter uniform higher order numerical treatment for singularly perturbed Robin type parabolic reaction diffusion multiple scale problems with large delay in time ⋮ A modification of the Shishkin discretization mesh for one-dimensional reaction-diffusion problems ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Discrete spline solution of singularly perturbed problem with two small parameters on a Shishkin-type mesh

Cites Work

• High order fitted operator numerical method for self-adjoint singular perturbation problems
• Robust convergence of a compact fourth-order finite difference scheme for reaction-diffusion problems
• A survey of numerical techniques for solving singularly perturbed ordinary differential equations
• High order parameter uniform numerical method for singular perturbation problems
• On a fourth-order finite-difference method for singularly perturbed boundary value problems
• High order methods for elliptic and time dependent reaction-diffusion singularly perturbed problems
• A priori meshes for singularly perturbed quasilinear two-point boundary value problems
• A Uniformly Accurate Finite-Element Method for a Singularly Perturbed One-Dimensional Reaction-Diffusion Problem
• A higher-order scheme for quasilinear boundary value problems with two small parameters
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