Improvement of numerical solution of self-adjoint singular perturbation problems by incorporation of asymptotic approximations

DOI10.1016/S0096-3003(97)10167-9zbMath0940.65080OpenAlexW2064164696MaRDI QIDQ1294321

K. Appert

Publication date: 19 July 2000

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

Full work available at URL: https://doi.org/10.1016/s0096-3003(97)10167-9

zbMATH Keywords

singular perturbationerror estimatesnumerical examplesfinite difference schemeasymptotic approximationnonlinear problemsbooster methodNewton quasi-linearization method

Mathematics Subject Classification ID

Nonlinear boundary value problems for ordinary differential equations (34B15) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70) Singular perturbations for ordinary differential equations (34E15) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (12)

“Booster method” for singularly perturbed robin problems i ⋮ A Robust computational method for singularly perturbed coupled system of reaction-diffusion boundary-value problems ⋮ Parameter uniform numerical method for third order singularly perturbed turning point problems exhibiting boundary layers ⋮ Improvement of numerical solution by boundary value technique for singularly perturbed one dimensional reaction diffusion problem. ⋮ Booster method for singularly-perturbed one-dimensional reaction-diffusion Neumann problems ⋮ Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection-diffusion problems on shishkin mesh ⋮ Non-polynomial spline solution of singularly perturbed boundary-value problems ⋮ “booster method” for singularly perturbed robin problems-II ⋮ Solving the modified regularized long wave equations via higher degree B-spline algorithm ⋮ A uniformly convergent hybrid scheme for singularly perturbed system of reaction-diffusion Robin type boundary-value problems ⋮ Numerical Solution of Singularly Perturbed Two-point BVPs Using Nonuniform Haar Wavelets ⋮ A computational method for self-adjoint singular perturbation problems using quintic spline

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solving singularly perturbed boundary-value problems by spline in tension
• Uniform fourth order difference scheme for a singular perturbation problem
• A boundary value technique for singular perturbation problems
• Improvement of numerical solution of boundary layer problems by incorpotation of asymptotic approximations
• Singular perturbation methods for ordinary differential equations
• Parallel initial-value algorithms for singularly perturbed boundary-value problems
• Initial-value methods for second-order singularly perturbed boundary- value problems
• An almost fourth order uniformly convergent difference scheme for a semilinear singularly perturbed reaction-diffusion problem
• Nonlinear singular perturbation phenomena: theory and applications
• A Uniformly Accurate Finite-Element Method for a Singularly Perturbed One-Dimensional Reaction-Diffusion Problem
• A difference scheme on a non-uniform mesh for a differential equation with a small parameter in the highest derivative
• The Numerical Solution of Boundary Value Problems for Stiff Differential Equations
• A variational difference scheme for a boundary value problem with a small parameter in the highest derivative
• On a Differential Equation of Boundary Layer Type

This page was built for publication: Improvement of numerical solution of self-adjoint singular perturbation problems by incorporation of asymptotic approximations