Journal ArticleDOI
An asymptotic finite element method for singularly perturbed third and fourth order ordinary differential equations with discontinuous source term
A. Ramesh Babu,N. Ramanujam +1 more
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TLDR
In this paper a computational method named as ''An asymptotic finite element method'' for solving singularly perturbed Boundary Value Problems (BVPs) with discontinuous source term and a small positive parameter multiplying the highest derivative is presented.About:
This article is published in Applied Mathematics and Computation.The article was published on 2007-08-01. It has received 16 citations till now. The article focuses on the topics: Method of matched asymptotic expansions & Partial differential equation.read more
Citations
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A brief survey on numerical methods for solving singularly perturbed problems
Mohan K. Kadalbajoo,Vikas Gupta +1 more
TL;DR: This survey paper contains a surprisingly large amount of literature on singularly perturbed problems and indeed can serve as an introduction to some of the ideas and methods for the singular perturbation problems.
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A review on singularly perturbed differential equations with turning points and interior layers
TL;DR: This paper reviews some existing literature on asymptotic and numerical analysis of singularly perturbed turning point and interior layer problems to find out what problems are treated and what numerical/asymptotic methods are employed, with an eye towards developing general methods to solve such problems.
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Approximate analytical solutions of singularly perturbed fourth order boundary value problems using differential transform method
TL;DR: In this paper, a reliable algorithm is presented to develop approximate analytical solutions of fourth order singularly perturbed two-point boundary value problems in which the highest order derivative is multiplied by a small parameter.
Solution of Fourth Order Singularly Perturbed Boundary Value Problem Using Septic Spline
Ghazala Akram,Afia Naheed +1 more
TL;DR: In this article, the fourth order singularly perturbed boundary value problem is solved using septic spline and the given method is proved to be fourth order convergent and compared with the existing method is evident that the method is better than the existing one.
References
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Book
Introduction to Perturbation Methods
TL;DR: The WKB and Related Methods are described and the method of Homogenization is explained, followed by a discussion of the properties of Transition Layer Equations and asymptotic approximations.
Book
Singular perturbation methods for ordinary differential equations
TL;DR: In this paper, a monograph on applications of mathematics is intended for students of mathematics, engineering and the sciences, which is intended to provide the basis for the reader to go on to solve new problems.
Book
Robust Computational Techniques for Boundary Layers
TL;DR: In this paper, numerical methods for problems with Boundary Layers are presented. But they do not address the problems with Frictionless Walls and No Slip Boundary Conditions, and they are not suitable for Non-Monotone Methods in two dimensions.
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V. Shanthi,N. Ramanujam +1 more