Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems

DOI10.1016/j.cam.2015.04.034zbMath1321.65126OpenAlexW2163017860MaRDI QIDQ492040

Pratibhamoy Das

Publication date: 19 August 2015

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.2015.04.034

zbMATH Keywords

singular perturbationnumerical experimentadaptive mesh generationmoving mesh methodsmesh equidistributiona posteriori meshesa priori meshesuniformly convergent adaptive solution

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular perturbations for ordinary differential equations (34E15) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Numerical solution of singularly perturbed problems involving ordinary differential equations (65L11)

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Cites Work

• A note on a parameterized singular perturbation problem
• A parallel boundary value technique for singularly perturbed two-point boundary value problems
• A rational spectral collocation method for solving a class of parameterized singular perturbation problems
• A second-order difference scheme for a parameterized singular perturbation problem
• A second-order hybrid finite difference scheme for a system of singularly perturbed initial value problems
• Uniform difference method for parameterized singularly perturbed delay differential equations
• A ``booster method for singular perturbation problems arising in chemical reactor theory
• Parametrized singularly perturbed boundary value problems
• HODIE finite difference schemes on generalized Shishkin meshes.
• Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: Analysis of convergence
• Uniform difference method for a parameterized singular perturbation problem
• Maximum norm a posteriori error estimates for a singularly perturbed differential difference equation with small delay
• A novel method for a class of parameterized singularly perturbed boundary value problems
• An efficient numerical method for singular perturbation problems
• Richardson Extrapolation Method for SingularlyPerturbed Convection-Diffusion Problems on AdaptivelyGenerated Mesh
• Convergence of de Boor's algorithm for the generation of equidistributing meshes
• Robust Numerical Methods for Singularly Perturbed Differential Equations
• A Constructive Theorem of Existence and Uniqueness for the Problem\documentclass{article}\pagestyle{empty}\begin{document}$ y' = f(x,y,\lambda),y(a) = \alpha,y\left( b\right) = \beta $\end{document}
• A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem
• Adaptive mesh generation for singularly perturbed fourth-order ordinary differential equations
• A new algorithm appropriate for solving singular and singularly perturbed autonomous initial-value problems

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