Numerical Solution Of Nonlinear Boundary Value Problems With Applications

Author : Milan Kubicek,Vladimir Hlavacek
Publisher : Courier Corporation
Page : 338 pages
File Size : 48,5 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780486463001

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Numerical Solution of Nonlinear Boundary Value Problems with Applications by Milan Kubicek,Vladimir Hlavacek Pdf

A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.

Author : Uri M. Ascher,Robert M. M. Mattheij,Robert D. Russell
Publisher : SIAM
Page : 620 pages
File Size : 54,9 Mb
Release : 1994-12-01
Category : Mathematics
ISBN : 1611971233

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Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by Uri M. Ascher,Robert M. M. Mattheij,Robert D. Russell Pdf

This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.

Author : A.K. Aziz
Publisher : Academic Press
Page : 380 pages
File Size : 48,8 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483267999

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Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations by A.K. Aziz Pdf

Numerical Solutions of Boundary Value Problems for Ordinary Differential Equations covers the proceedings of the 1974 Symposium by the same title, held at the University of Maryland, Baltimore Country Campus. This symposium aims to bring together a number of numerical analysis involved in research in both theoretical and practical aspects of this field. This text is organized into three parts encompassing 15 chapters. Part I reviews the initial and boundary value problems. Part II explores a large number of important results of both theoretical and practical nature of the field, including discussions of the smooth and local interpolant with small K-th derivative, the occurrence and solution of boundary value reaction systems, the posteriori error estimates, and boundary problem solvers for first order systems based on deferred corrections. Part III highlights the practical applications of the boundary value problems, specifically a high-order finite-difference method for the solution of two-point boundary-value problems on a uniform mesh. This book will prove useful to mathematicians, engineers, and physicists.

Author : Herbert B. Keller
Publisher : SIAM
Page : 69 pages
File Size : 50,6 Mb
Release : 1976-01-01
Category : Mathematics
ISBN : 161197044X

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Numerical Solution of Two Point Boundary Value Problems by Herbert B. Keller Pdf

Lectures on a unified theory of and practical procedures for the numerical solution of very general classes of linear and nonlinear two point boundary-value problems.

Author : István Faragó,János Karátson
Publisher : Nova Publishers
Page : 424 pages
File Size : 40,6 Mb
Release : 2002
Category : Mathematics
ISBN : 1590333764

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Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators by István Faragó,János Karátson Pdf

Numerical Solution of Nonlinear Elliptic Problems Via Preconditioning Operators - Theory & Applications

Author : Lakshmikantham
Publisher : Academic Press
Page : 385 pages
File Size : 51,7 Mb
Release : 1974-05-31
Category : Computers
ISBN : 9780080956183

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An Introduction to Nonlinear Boundary Value Problems by Lakshmikantham Pdf

A book on an advanced level that exposes the reader to the fascinating field of differential equations and provides a ready access to an up-to-date state of this art is of immense value. This book presents a variety of techniques that are employed in the theory of nonlinear boundary value problems. For example, the following are discussed: methods that involve differential inequalities; shooting and angular function techniques; functional analytic approaches; topological methods.

Author : Goong Chen,Jianxin Zhou
Publisher : Springer Science & Business Media
Page : 715 pages
File Size : 49,5 Mb
Release : 2010-09-01
Category : Mathematics
ISBN : 9789491216275

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BOUNDARY ELEMENT METHODS WITH APPLICATIONS TO NONLINEAR PROBLEMS by Goong Chen,Jianxin Zhou Pdf

Boundary Element Methods have become a major numerical tool in scientific and engineering problem-solving, with particular applications to numerical computations and simulations of partial differential equations in engineering. Boundary Element Methods provides a rigorous and systematic account of the modern mathematical theory of Boundary Element Methods, including the requisite background on general partial, differential equation methods, Sobolev spaces, pseudo-differential and Fredholm operators and finite elements. It aims at the computation of many types of elliptic boundary value problems in potential theory, elasticity, wave propagation, and structural mechanics. Also presented are various methods and algorithms for nonlinear partial differential equations. This second edition has been fully revised and combines the mathematical rigour necessary for a full understanding of the subject, with extensive examples of applications illustrated with computer graphics. This book is intended as a textbook and reference for applied mathematicians, physical scientists and engineers at graduate and research level. It will be an invaluable sourcebook for all concerned with numerical modeling and the solution of partial differential equations.

Author : Anonim
Publisher : Academic Press
Page : 322 pages
File Size : 44,8 Mb
Release : 1973-08-15
Category : Mathematics
ISBN : 0080956092

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Initial Value Methods for Boundary Value Problems: Theory and Application of Invariant Imbedding by Anonim Pdf

In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

Author : Sujaul Chowdhury,Syed Badiuzzaman Faruque,Ponkog Kumar Das
Publisher : Chapman & Hall/CRC
Page : 102 pages
File Size : 50,7 Mb
Release : 2021-10-25
Category : Mathematics
ISBN : 1003204910

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Numerical Solutions of Boundary Value Problems of Non-Linear Differential Equations by Sujaul Chowdhury,Syed Badiuzzaman Faruque,Ponkog Kumar Das Pdf

The book presents in comprehensive detail numerical solutions to boundary value problems of a number of non-linear differential equations. Replacing derivatives by finite difference approximations in these differential equations leads to a system of non-linear algebraic equations which we have solved using Newton's iterative method. In each case, we have also obtained Euler solutions and ascertained that the iterations converge to Euler solutions. We find that, except for the boundary values, initial values of the 1st iteration need not be anything close to the final convergent values of the numerical solution. Programs in Mathematica 6.0 were written to obtain the numerical solutions.

Author : Paul W. Eloe,Johnny Henderson
Publisher : World Scientific
Page : 249 pages
File Size : 51,7 Mb
Release : 2016
Category : Mathematics
ISBN : 9789814733489

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Nonlinear Interpolation and Boundary Value Problems by Paul W. Eloe,Johnny Henderson Pdf

"This book is devoted to the study of solutions of nonlinear ODE boundary value problems as nonlinear interpolation problems. In 1967, Lasota and Opial showed that, under suitable hypotheses, if solutions of a second-order nonlinear differential equation passing through two distinct points are unique, when they exist, then, in fact, a solution passing through two distinct points does exist. That result, coupled with the pioneering work of Philip Hartman on what was then called unrestricted n-parameter families has stimulated 50 years of rapid development in the study of solutions of boundary value problems as nonlinear interpolation problems. The purpose of this book is two-fold. First, the results that have been generated in the past 50 years are collected for the first time to produce a comprehensive and coherent treatment of what is now a well-defined area of study in the qualitative theory of ordinary differential equations. Second, methods and technical tools are sufficiently exposed so that the interested reader can contribute to the study of nonlinear interpolation"--

Author : M Ronto,A M Samoilenko
Publisher : World Scientific
Page : 468 pages
File Size : 41,9 Mb
Release : 2000-06-30
Category : Mathematics
ISBN : 9789814495486

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Numerical-Analytic Methods in the Theory of Boundary-Value Problems by M Ronto,A M Samoilenko Pdf

This book contains the main results of the authors' investigations on the development and application of numerical-analytic methods for ordinary nonlinear boundary value problems (BVPs). The methods under consideration provide an opportunity to solve the two important problems of the BVP theory — namely, to establish existence theorems and to build approximation solutions. They can be used to investigate a wide variety of BVPs. The Appendix, written in collaboration with S I Trofimchuk, discusses the connection of the new method with the classical Cesari, Cesari–Hale and Lyapunov–Schmidt methods. Contents:Numerical-Analytic Method of Successive Approximations for Two-Point Boundary-Value ProblemsModification of the Numerical-Analytic Method for Two-Point Boundary-Value ProblemsNumerical-Analytic Method for Boundary-Value Problems with Parameters in Boundary ConditionsCollocation Method for Boundary-Value Problems with ImpulsesThe Theory of the Numerical-Analytic Method: Achievements and New Trends of Development Readership: Researchers on differential equations. Keywords:Ordinary Differential Equations;Nonlinear Boundary Value Problems;Periodic Boundary Value Problems;Nonlinear Boundary Conditions;Parametrized Boundary Value Problems;Numerical-Analytic Method;Successive Approximations;Determining Equations;Trigonometric Collocation;Impulsive Systems

Author : Christopher T. H. Baker,Chris Phillips
Publisher : Oxford University Press, USA
Page : 392 pages
File Size : 50,9 Mb
Release : 1981
Category : Language Arts & Disciplines
ISBN : UCAL:B4980150

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The Numerical Solution of Nonlinear Problems by Christopher T. H. Baker,Chris Phillips Pdf

Author : Dumitru Motreanu,Viorica Venera Motreanu,Nikolaos Papageorgiou
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 43,6 Mb
Release : 2013-11-19
Category : Mathematics
ISBN : 9781461493235

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Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems by Dumitru Motreanu,Viorica Venera Motreanu,Nikolaos Papageorgiou Pdf

This book focuses on nonlinear boundary value problems and the aspects of nonlinear analysis which are necessary to their study. The authors first give a comprehensive introduction to the many different classical methods from nonlinear analysis, variational principles, and Morse theory. They then provide a rigorous and detailed treatment of the relevant areas of nonlinear analysis with new applications to nonlinear boundary value problems for both ordinary and partial differential equations. Recent results on the existence and multiplicity of critical points for both smooth and nonsmooth functional, developments on the degree theory of monotone type operators, nonlinear maximum and comparison principles for p-Laplacian type operators, and new developments on nonlinear Neumann problems involving non-homogeneous differential operators appear for the first time in book form. The presentation is systematic, and an extensive bibliography and a remarks section at the end of each chapter highlight the text. This work will serve as an invaluable reference for researchers working in nonlinear analysis and partial differential equations as well as a useful tool for all those interested in the topics presented.

Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Page : 158 pages
File Size : 45,9 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9783036507101

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Nonlinear Differential Equations and Dynamical Systems by Feliz Manuel Minhós,João Fialho Pdf

This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.

Author : You-He Zhou
Publisher : Springer Nature
Page : 478 pages
File Size : 42,9 Mb
Release : 2021-03-09
Category : Technology & Engineering
ISBN : 9789813366435

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Wavelet Numerical Method and Its Applications in Nonlinear Problems by You-He Zhou Pdf

This book summarizes the basic theory of wavelets and some related algorithms in an easy-to-understand language from the perspective of an engineer rather than a mathematician. In this book, the wavelet solution schemes are systematically established and introduced for solving general linear and nonlinear initial boundary value problems in engineering, including the technique of boundary extension in approximating interval-bounded functions, the calculation method for various connection coefficients, the single-point Gaussian integration method in calculating the coefficients of wavelet expansions and unique treatments on nonlinear terms in differential equations. At the same time, this book is supplemented by a large number of numerical examples to specifically explain procedures and characteristics of the method, as well as detailed treatments for specific problems. Different from most of the current monographs focusing on the basic theory of wavelets, it focuses on the use of wavelet-based numerical methods developed by the author over the years. Even for the necessary basic theory of wavelet in engineering applications, this book is based on the author’s own understanding in plain language, instead of a relatively difficult professional mathematical description. This book is very suitable for students, researchers and technical personnel who only want to need the minimal knowledge of wavelet method to solve specific problems in engineering.