Spline techniques for solving singularly-perturbed nonlinear problems on nonuniform grids

DOI10.1023/A:1016023012671zbMath1032.65083OpenAlexW1511521728MaRDI QIDQ1862195

Mohan K. Kadalbajoo, Kailash C. Patidar

Publication date: 10 March 2003

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1016023012671

zbMATH Keywords

convergencenumerical examplessingular perturbationsdifference schemesquasilinearizationnonlinear equationcubic splinesboundary-value problemsnonuniform gridvariable-mesh

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) Finite difference and finite volume methods for ordinary differential equations (65L12) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)

Related Items (10)

Numerical methods on Shishkin mesh for singularly perturbed delay differential equations with a grid adaptation strategy ⋮ An efficient numerical technique for solving nonlinear singularly perturbed reaction diffusion problem ⋮ A parameter-uniform B-spline collocation method for singularly perturbed semilinear reaction-diffusion problems ⋮ B-splines with artificial viscosity for solving singularly perturbed boundary value problems ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ The impact of smooth \(W\)-grids in the numerical solution of singular perturbation two-point boundary value problems ⋮ Uniform global convergence of a hybrid scheme for singularly perturbed reaction-diffusion systems ⋮ B-spline collocation method for nonlinear singularly-perturbed two-point boundary-value problems ⋮ Fractal quintic spline method for nonlinear boundary-value problems ⋮ Numerical solution of singularly perturbed convection-diffusion problem using parameter uniform B-spline collocation method

Cites Work

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• A collocation method for singularly perturbed two-point boundary value problems with splines in tension
• Nonstandard finite difference equations for ODEs and 1-D PDEs based on piecewise linearization
• Galerkin-Petrov method for strongly nonlinear singularly perturbed boundary value problems on special meshes
• Singular perturbations in systems and control. (Seminar held in Udine, Italy, 1982)
• Nonlinear singular perturbation phenomena: theory and applications
• A Priori Estimates and Analysis of a Numerical Method for a Turning Point Problem
• Collocation for Singular Perturbation Problems III: Nonlinear Problems without Turning Points
• A Deferred Correction Method for Nonlinear Two-Point Boundary Value Problems: Implementation and Numerical Evaluation
• An Adaptive Shooting Method for Singularly Perturbed Boundary Value Problems
• On the Numerical Integration of Nonlinear Two-Point Boundary Value Problems Using Iterated Deferred Corrections. Part 2: The Development and Analysis of Highly Stable Deferred Correction Formulae
• Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
• Numerical Methods for Singular Perturbation Problems
• An Analysis of a Uniformly Accurate Difference Method for a Singular Perturbation Problem
• Singular perturbations and differential inequalities
• Boundary-interior layer interactions in nonlinear singular perturbation theory
• Monotone Difference Schemes for Singular Perturbation Problems

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