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Sunday, May 17, 2020 | History

1 edition of Fitted Numerical Methods for Singular Perturbation Problems found in the catalog.

Fitted Numerical Methods for Singular Perturbation Problems

error estimates in the maximum norm for linear problems in one and two dimensions

by J. J. H. Miller

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  • 5 Currently reading

Published by World Scientific in Singapore .
Written in English


About the Edition

Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. This book offers an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations. It can be used as an introductory text to the theory underpinning fitted mesh methods.

Edition Notes

ContributionsO"Riordan, E., Shishkin, G. I.
The Physical Object
Pagination176 s.
Number of Pages176
ID Numbers
Open LibraryOL27039002M
ISBN 109814390739
ISBN 109789814390736
OCLC/WorldCa818387654

For some numerical methods one may refer to recent books: Miller [6], Hemker and Miller [3], Doolan et al. [2]. In this paper an exponentially fitted finite difference method is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at one end (left or right) by: More discussions on fitted and some other numerical methods for singular perturbation problems can be referred in,,,,. In this paper a fourth-order tridiagonal finite difference scheme is presented for solving singularly perturbed two-point boundary value problems with the boundary layer at Cited by:

Elementary Lectures on Numerical Methods for Singular Perturbation Problems 3 In order to discuss numerical solutions we need to discretise the domain Ω = (0, X ]. H. S. Prasad and Y. N. Reddy [3] considered Differential Quadrature Method for finding the numerical solution of boundary-value problems for a singularly perturbed differential-difference equation of mixed type. In recent papers [] the terms negative or left shift and positive or right shift have been used for delay and advance by: 2.

Buy Computational Methods for a Class of Singular Perturbation Problems: Numerical treatment for a class of singular Perturbation Problems on FREE SHIPPING on qualified orders. This paper deals with a numerical method with fitted operator difference method for twin (dual) boundary layers singularly perturbed boundary value problems. Asymptotic and numerical analysis of singular perturbation problems: A survey, Applied Mathematics and Computation 30(3) (), – , DOI: /(89) J. J. H Author: S. Rakmaiah, K. Phaneendra.


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Fitted Numerical Methods for Singular Perturbation Problems by J. J. H. Miller Download PDF EPUB FB2

Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple.

This book can be used as an introductory text to the theory underpinning fitted mesh : John J H Miller, Eugene O'Riordan, G I Shishkin. Fitted Numerical Methods for Singular Perturbation Problems. Since the first edition of this book the literature on fitted mesh methods for singularly perturbed problems has expanded significantly.

Over the intervening years, fitted meshes have been shown to be effective for an extensive set of singularly perturbed partial differential equations. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems.

The global errors in the numerical approximations are measured in the pointwise maximum norm. Fitted Numerical Methods For Singular Perturbation Problems Since the first edition of this book, the literature on fitted mesh methods for singularly perturbed problems has expanded significantly.

Over the intervening years, fitted meshes have been shown to be effective Fitted Numerical Methods for Singular Perturbation Problems book an extensive set of singularly perturbed partial differential equations.

Fitted Numerical Methods For Singular Perturbation Problems Since the first edition of this book the literature on fitted mesh methods for singularly perturbed problems has expanded significantly.

Over the intervening years, fitted meshes have been shown to be effective for an extensive set of. Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems.

The global errors in the numerical approximations are measured in the pointwise maximum norm. The fitted mesh algorithm is particularly simple to implement in practice, but the theory of why these numerical methods work is far from simple. This book can be used as an introductory text to the theory underpinning fitted mesh by: This will serve to introduce the main ideas which in subsequent chapters are applied to problems of increasing generality.

The additional function spaces required are L p (Ω) = {f: (∫ Ω |f(x)| p dx) 1/p }, 1 ≤ p where Ω is any bounded open domain in ℝ. () An Adaptive Uniformly Convergent Numerical Method for a Semilinear Singular Perturbation Problem.

SIAM Journal on Numerical AnalysisAbstract | PDF ( KB)Cited by: Boundary Layers and Singular Perturbation Lectures 16 and 17 Boundary Layers and Singular Perturbation A Regular Perturbation In some physical problems, the solution is dependent on a parameter K.

When the parameter K is very small, it is natural to expect that the solution not be very different from the one with K set to Size: KB. In all cases a piecewise uniform fitted mesh turns out to be sufficient for the construction of an ε-uniform method.

Of course, more complicated meshes may also be used, but the simplicity of the piecewise uniform meshes is considered to be one of their major attractions. In these special numerical methods, the grid equations are solved on the simplest piecewise-uniform grids which are known in the literature on numerical methods for singularly perturbed problems.

Doolen et al. [5] have presented various exponentially fitted finite difference schemes, for both initial and boundary layer problems which are uniformly convergent in E. Lorenz [6] has proposed a combination of initial and boundary value methods to solve singular perturbation by: In the revised version of this book, the reader will find an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations.

Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems. ISBN: OCLC Number: Description: xiv, pages: illustrations ; 23 cm: Contents: 1. Motivation for the study of singular perturbation problems Simple examples of singular perturbation problems Numerical methods for singular perturbation problems Simple fitted operator methods in one dimension Simple fitted mesh methods in one.

3 Numerical methods for singular perturbation problems 11 4 Simple fitted operator methods in one dimension 18 5 Simple fitted mesh methods in one dimension 30 6 Convergence of fitted mesh finite difference methods for linear reaction-diffusion problems in one dimension 38 7 Properties of upwind finite difference operators on piecewise uniform.

Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions (Revised Edition). Fitted mesh methods focus on the appropriate distribution of the mesh points for singularly perturbed problems.

This book offers an introduction to the basic theory associated with fitted numerical methods for singularly perturbed differential equations.

It can be used as an introductory text to the theory underpinning fitted mesh methods. ISBN: OCLC Number: Description: 1 online resource: illustrations: Contents: 1.

Motivation for the study of singular perturbation problems Simple examples of singular perturbation problems Numerical methods for singular perturbation problems Simple fitted operator methods in one dimension Simple fitted mesh methods in.

The scheme thus derived is fourth order accurate for moderate values of the perturbation parameter ε whereas for very small values of this parameter the method is “ ε-uniformly convergent with order two”.

Numerical examples are given in support of the by: Bail V: Proceedings Of The Fifth International Conference On Boundary And Interior Layers: Computational And Asymptotic Methods: 20 24 June,Shanghai, China.

1. Motivation for the study of singular perturbation problems Simple examples of singular perturbation problems Numerical methods for singular perturbation problems Simple fitted operator methods in one dimension Simple fitted mesh methods in one dimension A fitted mesh method for our simple initial value problem is constructed.

It is proved rigorously that this method is parameter-uniform at the mesh points. Finally, in the fourth section, numerical solutions of singular perturbation problems are discussed. Computations using standard and a parameter-uniform numerical method are : John J.

H. Miller.Numerical Methods for Singular Perturbation Problems; Simple Fitted Operator Methods in One Dimension; Simple Fitted Mesh Methods in One Dimension; Convergence of Fitted Mesh Difference Methods for Linear Reaction-Diffusion Problems in One Dimension; Properties of Upwind Finite Difference Operators on Piecewise Uniform Fitted Meshes.