Exponential B-spline collocation method for self-adjoint singularly perturbed boundary value problems

DOI10.1016/j.apnum.2007.09.008zbMath1157.65047OpenAlexW2080305533MaRDI QIDQ947748

Mukesh Kumar, S. Chandra Sekhara Rao

Publication date: 7 October 2008

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2007.09.008

zbMATH Keywords

convergencecollocation methodsingular perturbationnumerical experimentsexponential boundary layersexponential B-splinesecond order linear differential equationuniform meshself-adjoint boundary value problem

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05) Singular perturbations for ordinary differential equations (34E15)

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Cites Work

• Unnamed Item
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• Singularly perturbed finite element methods
• Theory of exponential splines
• A lower bound for the smallest singular value of a matrix
• Properties of splines in tension
• A practical guide to splines
• Fitted mesh \(B\)-spline collocation method for solving self-adjoint singularly perturbed boundary value problems
• Optimal B-spline collocation method for self-adjoint singularly perturbed boundary value problems
• A Uniformly Accurate Finite-Element Method for a Singularly Perturbed One-Dimensional Reaction-Diffusion Problem
• On the Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems in Two and One Dimensions
• A Uniformly Accurate Finite Element Method for a Singular Perturbation Problem in Conservative Form
• An Analysis of a Superconvergence Result for a Singularly Perturbed Boundary Value Problem
• Alternatives to the Exponential Spline in Tension
• An Interpolation Curve Using a Spline in Tension

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