Numerical solution of nonlinear singularly perturbed problems on nonuniform meshes by using a non-standard algorithm

DOI10.1007/s10910-009-9625-2zbMath1304.65180OpenAlexW2091065995MaRDI QIDQ1959263

Higinio Ramos, M. A. Queiruga, Srinivasan Natesan, Jesus Vigo Aguiar, Raquel García Rubio

Publication date: 6 October 2010

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10910-009-9625-2

zbMATH Keywords

nonuniform meshespiecewise-uniform Shishkin meshnon-standard algorithmsingularly perturbed initial-value problems

Mathematics Subject Classification ID

Classical flows, reactions, etc. in chemistry (92E20) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

Related Items (31)

Using the blow-up technique for a modified Lindemann mechanism ⋮ Higher order computational method for a singularly perturbed nonlinear system of differential equations ⋮ Parameter uniform numerical method for third order singularly perturbed turning point problems exhibiting boundary layers ⋮ Efficient High-Order Discretization Methods for Coupled Systems of Singularly Perturbed Parabolic Convection-Diffusion Problems ⋮ An efficient finite difference method for coupled systems of singularly perturbed parabolic convection-diffusion problems ⋮ Optimal fourth-order parameter-uniform convergence of a non-monotone scheme on equidistributed meshes for singularly perturbed reaction–diffusion problems ⋮ An adaptive moving grid method for a system of singularly perturbed initial value problems ⋮ Parameter uniform optimal order numerical approximation of a class of singularly perturbed system of reaction diffusion problems involving a small perturbation parameter ⋮ Parameter uniform higher order numerical treatment for singularly perturbed Robin type parabolic reaction diffusion multiple scale problems with large delay in time ⋮ Unnamed Item ⋮ Computational cost reduction for coupled system of multiple scale reaction diffusion problems with mixed type boundary conditions having boundary layers ⋮ A domain decomposition method of Schwarz waveform relaxation type for singularly perturbed nonlinear parabolic problems ⋮ A parameter-uniform numerical method for singularly perturbed Robin type parabolic convection-diffusion turning point problems ⋮ Numerical solution of 2D singularly perturbed reaction-diffusion system with multiple scales ⋮ A finite difference method for a singularly perturbed 2‐D elliptic convection‐diffusion PDEs on Shishkin‐type meshes with non‐smooth convection and source terms ⋮ Numerical solution of a fourth‐order singularly perturbed boundary value problem with discontinuities via Haar wavelets ⋮ A variable stepsize hybrid block optimized technique for integrating a class of singularly perturbed parabolic problems ⋮ A new 2-level implicit high accuracy compact exponential approximation for the numerical solution of nonlinear fourth order Kuramoto-Sivashinsky and Fisher-Kolmogorov equations ⋮ Numerical solution of nonlinear singularly perturbed problems by using a non-standard algorithm on variable stepsize implementation (CMMSE-2009) ⋮ Alternating direction numerical scheme for singularly perturbed 2D degenerate parabolic convection-diffusion problems ⋮ Additive schemes based domain decomposition algorithm for solving singularly perturbed parabolic reaction-diffusion systems ⋮ Quintic B-spline method for solving second order linear and nonlinear singularly perturbed two-point boundary value problems ⋮ A numerical method for singularly perturbed turning point problems with an interior layer ⋮ Four computational approaches for solving a class of boundary value problems arising in chemical reactor industry ⋮ A new approach to constructing of explicit one-step methods of high order for singular initial value problems for nonlinear ordinary differential equations ⋮ An efficient optimized adaptive step-size hybrid block method for integrating differential systems ⋮ A non-uniform difference scheme for solving singularly perturbed 1D-parabolic reaction-convection-diffusion systems with two small parameters and discontinuous source terms ⋮ Analysis of a nonlinear singularly perturbed Volterra integro-differential equation ⋮ An efficient numerical method for coupled systems of singularly perturbed parabolic delay problems ⋮ An effective numerical approach for two parameter time-delayed singularly perturbed problems ⋮ A comparative study on stabilized finite element methods for the convection-diffusion-reaction problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A Shishkin mesh for a singularly perturbed Riccati equation
• A parallel boundary value technique for singularly perturbed two-point boundary value problems
• Gas absorption with first order chemical reaction in a laminar falling film over a reacting solid wall
• Uniform and optimal schemes for stiff initial-value problems
• Initial-value technique for singularly perturbed boundary-value problems for second-order ordinary differential equations arising in chemical reactor theory
• A ``booster method for singular perturbation problems arising in chemical reactor theory
• A numerical algorithm for singular perturbation problems exhibiting weak boundary layers.
• A non-standard explicit integration scheme for initial-value problems
• Nonlinear boundary value problems suggested by chemical reactor theory
• A new algorithm appropriate for solving singular and singularly perturbed autonomous initial-value problems
• Multiple Stable Solutions of Nonlinear Boundary Value Problems Arising in Chemical Reactor Theory

This page was built for publication: Numerical solution of nonlinear singularly perturbed problems on nonuniform meshes by using a non-standard algorithm