6 edition of The Boundary Function Method for Singular Perturbed Problems (Studies in Applied and Numerical Mathematics) found in the catalog.
January 1, 1987
by Society for Industrial Mathematics
Written in English
|The Physical Object|
|Number of Pages||221|
C. G. Lange and R. M. Miura, Singular perturbation analysis of boundary-value problems for differential-difference equations V. Small shifts with layer behaviour, SIAM Journal on Applied Mathematics 54 (), – , DOI: /SAuthor: M. Adilaxmi, D. Bhargavi, K. Phaneendra. This paper presents a four point block one-step method for solving directly boundary value problems (BVP) with Neumann boundary conditions and Singular Perturnbation BVPs. This method is formulated using Lagrange interpolating polynomial. The block method will solve the second order linear Neumann and Singular Perturbation BVPs directly without reducing it to the system of first order Author: Mohd Mughti Hasni, Zanariah Abdul Majid, Norazak Senu, Sokkalingam Rajalingam, Hanita Daud, Muhamad.
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. In this 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.
Abstract: For a second-order singularly perturbed ordinary differential equation (ODE) under the Robin type boundary conditions, we develop an energetic Robin boundary functions method (ERBFM) to find the solution, which automatically satisfies the Robin boundary the non-singular ODE the Robin boundary functions consist of polynomials, while the normalized exponential trial. A Shooting Algorithm for Optimal Control Problems with Singular Arcs 3 conditions both in the initial and nal times. We de ne the shooting function as the mapping that assigns to each estimate of the initial values, the value of the nal condition of the corresponding solution. The shooting algorithm consists of approximating a zero of this.
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This book was written as a textbook on one of the effective asymptotic methods in the theory of singular perturbations, the boundary function arly perturbed equations are often used as mathematical models describing processes in physics, chemical kinetics, and mathematical biology, and they often arise during investigation of applied problems of technology and engineering.
The Boundary Function Method for Singular Perturbed Problems Adelaida B. Vasil’eva, Valentin F. Butuzov, Leonid V. Kalachev This is the first book published in English devoted solely to the boundary function method, which is one of the asymptotic methods.
ISBN: OCLC Number: Description: xiii, pages: illustrations ; 27 cm: Contents: 1. Basic Ideas. Regular and singular. Get this from a library. The boundary function method for singular perturbation problems.
[A B Vasilʹeva; V F Butuzov; Leonid V Kalachev; Society for Industrial and Applied Mathematics.] -- This is the first book published in English devoted solely to the boundary function method, which is one of the asymptotic methods.
This method provides an effective and simple way to obtain. In this paper, we study the numerical solution of singular singularly perturbed third-order boundary value problems (BVPs) by using Quartic B-spline method. An efficient algorithm is presented here to solve the approximate solution of the given problem.
To understand our method, we introduce the Quartic B-spline basis function in the form of at the different knots.
In the case of differential equations, boundary conditions cannot be satisfied; in algebraic equations, the possible number of solutions is decreased.
Singular perturbation theory is a rich and ongoing area of exploration for mathematicians, physicists, and other researchers. The methods used to tackle problems in this field are many. Here, we generalize the boundary layer functions method (or composite asymptotic expansion) for bisingular perturbed differential equations (BPDE that is perturbed differential equations with singular point).
We will construct a uniform valid asymptotic solution of the singularly perturbed first-order equation with a turning point, for BPDE of the Airy type and for BPDE of the second-order Author: Keldibay Alymkulov, Dilmurat Adbillajanovich Tursunov. A spline method for second-order singularly perturbed boundary-value problems Article in Journal of Computational and Applied Mathematics (2) October with 46 Reads.
Kumar and P. Singh  were used cubic-spline method to develop initial-value technique for second-order self-adjoint singular perturbation boundary value problems, while Ikram A. Tirmizi  Used Quartic non-polynomial spline function to solve this type of.
We consider a difference scheme based on cubic spline in compression for second-order singularly perturbed boundary value problem of the form εy″=p(x)y′+q(x)y+r(x), y(a)=α 0, y(b)=α 1. The method is shown to have second- and fourth-order convergence depending on the choice of parameters λ 1 and λ 2 involved in the method.
The method is tested on an example and the results found to be Cited by: For singular perturbation problems the aim is to cluster automatically grid points within a boundary layer and an obvious choice of adaptivity criterion is therefore the solution gradient [8, 10].
Buy The Boundary Function Method for Singular Perturbation Problems (Studies in Applied and Numerical Mathematics) by Vasil'eva, Adelaida B., Butuzov, Valentin F., Kalachev, Leonid V.
(ISBN: ) from Amazon's Book Store. Everyday low prices and free delivery on eligible : Adelaida B. Vasil'eva, Valentin F. Butuzov, Leonid V. Kalachev. for a second-order singularly perturbed ordinary differential equation (ODE) under the Robin type boundary conditions, we develop an energetic Robin boundary functions method (ERBFM) to find the solution, which automatically satisfies the Robin boundary conditions.
For the non-singular ODE the Robin boundary functions consist of polynomials Cited by: 1. A class of singularly perturbed boundary value problems arising in discrete systems with inputs is considered in state variable form.
It is found that the degenerate problem is unable to satisfy all the given boundary conditions. India A SINGULAR PERTURBATION METHOD FOR BOUNDARY VALUE PROBLEMS IN DISCRETE SYSTEMS D. Naidu and A Cited by: 1. The book contains seven chapters written by noted experts and young researchers who present their recent studies of both pure mathematical problems of perturbation theories and application of perturbation methods to the study of the important topic in physics, for example, renormalization group theory and applications to basic models in theoretical physics (Y.
Takashi), the quantum gravity and Cited by: 1. A singular perturbation problem is one for which the perturbed problem is qualitatively di erent from the unperturbed problem. One typically obtains an asymptotic, but possibly divergent, expansion of the solution, which depends singularly on the parameter ".
Although singular perturbation problems may appear atypical, they are the most. singular singularly perturbed boundary value problem. Remaining part of this paper is organized as follows: Section 2 describes the definition of basics of Quartic B-spline and value of its derivatives at nodal points.
In Section 3, the Quartic -spline method for thirdB -order singular singularly perturbed boundary value method is. It is noted that the method presented in is unsuited to solve the singularly perturbed problems with different widths of boundary layers.
The purpose of this paper is to study a new rational spectral collocation method in barycentric form for the above singularly perturbed convection-diffusion problems with two small parameters (1).Author: Ke-Zhong Lu, Li-Bin Liu, Honglin Fang, Lili Liu.
AMS subject classifications. 34K28, 34K26, 34K10 1. Introduction and examples. Boundary value problems for singularly perturbed differential difference equations are ubiquitous in the mathematical modeling of various practical phenomena in biology and physics, such as in variational problems in control theory and first exit time problems in the modeling of the determination of.
Abstract. This dissertation concerns the study of certain singularly perturbed boundary value problems. In the first part of this dissertation (Chapters 2 and 3), a singularly perturbed nonlinear system of differential equations are considered over a compact interval, subject to general boundary conditions that allow the coupling of the boundary values at the different endpoints.
Stojanovic, M.: Numerical solution of initial and singularly perturbed two-point boundary value problems using adaptive spline function approximation. Publications de L’institut Mathemati – () MathSciNet Google ScholarAuthor: Using Spline.perturbed boundary value problems, using finite element method .
Their collocation method was applied with quadratic and cubic B-spline base functions over the geometrically graded mesh of the solution domain. InRashidina and Mohammadi  considered the self-adjoint singularly perturbed two-point boundary value : W.
K. Zahra, M. A. El-Beltagy, A. M. El Mhlawy, R. R. Elkhadrawy. The numerical solution of singular perturbation problems (SPPs) is delicate because the perturbation parameter &; and the mesh size h cannot vary independently of one another.
In the extended abstract (J.M.-S. Lubuma, K.C. Patidar, Finite element methods for self-adjoint singular perturbation problems, in: T.E. Simos, G. Maroulis (Eds.), ICCMSE Advances in Computational .