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Journal ArticleDOI

Improvement of numerical solution of boundary layer problems by incorporation of asymptotic approximations

Moshe Israeli, +1 more
- 01 Oct 1982 - 
- Vol. 39, Iss: 3, pp 309-324
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TLDR
In this paper, a method for improvement of the numerical solution of differential equations by incorporation of asymptotic approximations is investigated for a class of singular perturbation problems, and uniform error estimates are derived for this method when implemented in known difference schemes and applied to linear second order O.D.E.'s.
Abstract: 
A method for improvement of the numerical solution of differential equations by incorporation of asymptotic approximations is investigated for a class of singular perturbation problems. Uniform error estimates are derived for this method when implemented in known difference schemes and applied to linear second order O.D.E.'s. An improvement by a factor of?n+1 can be obtained (where ? is the "small" parameter andn is the order of the asymptotic approximation) for a small amount of extra work. Numerical experiments are presented.

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Citations
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Journal ArticleDOI

A numerical method for boundary value problems for singularly perturbed fourth-order ordinary differential equations

V. Shanthi, +1 more
- 10 Jul 2002 - 
TL;DR: Newton's method of quasi-linearization is applied to solveSingularly perturbed two-point boundary value problems (BVPs) for fourth-order ordinary differential equations (ODEs) with a small positive parameter multiplying the highest derivative are considered.
Journal ArticleDOI

A “Booster method” for singular perturbation problems arising in chemical reactor theory

Srinivasan Natesan, +1 more
- 01 Apr 1999 - 
TL;DR: A numerical method for singularly perturbed two-point boundary-value problems (BVPs) for second-order ordinary differential equations (ODEs) arising in chemical reactor theory is proposed, and an asymptotic approximation is incorporated into a suitable finite difference scheme to improve the numerical solution.
Journal ArticleDOI

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

V. Shanthi, +1 more
- 15 Dec 2002 - 
TL;DR: In this paper, a singularly perturbed boundary value problem (BVP) with a small positive parameter multiplying the highest derivative of the [emailprotected]^i^v(x)-a(x)[email protected] was considered.
Journal ArticleDOI

Improvement of numerical solution of selfadjoint singular perturbation problems by incorporation of asymptotic approximations

Srinivasan Natesan, +1 more
- 01 Feb 1999 - 
TL;DR: A numerical method for singularly perturbed two-point boundary-value problems for second-order ordinary differential equations without a first derivative term arising in the study of chemical catalysis and Michaelis-Menten process in biology is proposed.
Journal ArticleDOI

An asymptotic finite element method for improvement of solutions of boundary layer problems

P Bar-Yoseph, +1 more
- 01 Aug 1986 - 
TL;DR: A scheme that uses singular perturbation theory to improve the performance of existing finite element methods is presented and improves the error bounds of the standard Galerkin finite element scheme by a factor of O(εn+1).
References
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Book

Perturbation Methods

Ali H. Nayfeh, +1 more
TL;DR: This website becomes a very available place to look for countless perturbation methods sources and sources about the books from countries in the world are provided.
Book

Perturbation methods in fluid mechanics

Milton van Dyke
Book

Perturbation Methods in Applied Mathematics

Julian D. Cole, +1 more
TL;DR: In this paper, limit process expansions applied to Ordinary Differential Equations (ODE) are applied to partial differential equations (PDE) in the context of Fluid Mechanics.
Book

Introduction to singular perturbations

Robert E. O'Malley
Journal ArticleDOI

Perturbation Methods in Applied Mathematics

H. Weitzner, +1 more
- 01 Jul 1969 - 
TL;DR: In this article, limit process expansions applied to Ordinary Differential Equations (ODE) are applied to partial differential equations (PDE) in the context of Fluid Mechanics.