Asymptotic numerical methods for singularly perturbed fourth-order ordinary differential equations of reaction-diffusion type

DOI10.1016/S0898-1221(03)90039-3zbMath1054.65078MaRDI QIDQ597243

Sumit K. Garg

Publication date: 6 August 2004

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

zbMATH Keywords

maximum principlesingular perturbationfinite difference methodasymptotic expansionsboundary layerreaction-diffusion equationfourth-order ordinary differential equationboundary value techniquefitted mesh methodfitted operator methodstability issues

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) 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) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (14)

Formation of boundary layers for singularly perturbed fourth-order ordinary differential equations with the Lidstone boundary conditions ⋮ A mini-review of numerical methods for high-order problems† ⋮ Solving a singular beam equation by using a weak-form integral equation method ⋮ An efficient superconvergent spline collocation algorithm for solving fourth order singularly perturbed problems ⋮ Solving a singular beam equation by the method of energy boundary functions ⋮ A numerical method for singularly perturbed weakly coupled system of two second order ordinary differential equations with discontinuous source term ⋮ A brief survey on numerical methods for solving singularly perturbed problems ⋮ Uniformly convergent scheme for fourth-order singularly perturbed convection-diffusion ODE ⋮ An asymptotic numerical method for fourth order singular perturbation problems with a discontinuous source term ⋮ Computational methods for reaction--diffusion problems for fourth order ordinary differential equations with a small parameter at the highest derivative. ⋮ Superconvergence of conforming finite element for fourth‐order singularly perturbed problems of reaction diffusion type in 1D ⋮ A recent survey on computational techniques for solving singularly perturbed boundary value problems ⋮ A boundary value technique for boundary value problems for singularly perturbed fourth-order ordinary differential equations ⋮ Approximate analytical solution of fourth order boundary value problems

Cites Work

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• Numerical treatment of singularly perturbed two point boundary value problems
• Approximate method for the numerical solution of singular perturbation problems
• Numerical solution of singular perturbation problems via deviating arguments
• Die gleichmäßige Stabilität singulär gestörter diskreter und kontinuierlicher Randwertprobleme
• Further examples of the boundary value technique in singular perturbation problems
• Singular perturbation problems for systems of partial differential equations of elliptic type
• A boundary value technique for singular perturbation problems
• A computational method for solving singularly perturbed turning point problems exhibiting twin boundary layers
• A numerical method for singular perturbation problems arising in chemical reactor theory
• Singularly perturbed higher order boundary value problems
• A computational method for solving singular perturbation problems
• Singular perturbations of boundary value problems for a class of third order nonlinear ordinary differential equations
• The Asymptotic Solution of a Class of Third-Order Boundary Value Problems Arising in the Theory of Thin Film Flows
• Graded-Mesh Difference Schemes for Singularly Perturbed Two-Point Boundary Value Problems
• Sufficient Conditions for Uniform Convergence of a Class of Difference Schemes for a Singularly Perturbed Problem
• Differential Inequalities of Higher Order and the Asymptotic Solution of Nonlinear Boundary Value Problems
• Locking in finite-element approximations to long thin extensible beams
• Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: reaction-diffusion-type problems

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