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An Introduction to Nonlinear Boundary Value Problems
Author: Lakshmikantham
Publisher: Academic Press
Published: 1974-05-31
Total Pages: 385
ISBN-13: 0080956181
DOWNLOAD EBOOK →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.
A Modified Quasilinearization Concept for Solving the Nonlinear Two-point Boundary Value Problem
Numerical Solution of Nonlinear Boundary Value Problems with Applications
Author: Milan Kubicek
Publisher: Courier Corporation
Published: 2008-01-01
Total Pages: 338
ISBN-13: 0486463001
DOWNLOAD EBOOK →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.
Generalized Quasilinearization for Nonlinear Problems
Author: V. Lakshmikantham
Publisher: Springer Science & Business Media
Published: 2013-03-14
Total Pages: 287
ISBN-13: 1475728743
DOWNLOAD EBOOK →The book provides a systematic development of generalized quasilinearization indicating the notions and technical difficulties that are encountered in the unified approach. It enhances considerably the usefulness of the method of quasilinearization which has proved to be very effective in several areas of investigation and in applications. Further it includes the well-known monotone iterative technique as a special case. Audience: Researchers, industrial and engineering scientists.
Analytical Solution Methods for Boundary Value Problems
Author: A.S. Yakimov
Publisher: Academic Press
Published: 2016-08-13
Total Pages: 200
ISBN-13: 0128043636
DOWNLOAD EBOOK →Analytical Solution Methods for Boundary Value Problems is an extensively revised, new English language edition of the original 2011 Russian language work, which provides deep analysis methods and exact solutions for mathematical physicists seeking to model germane linear and nonlinear boundary problems. Current analytical solutions of equations within mathematical physics fail completely to meet boundary conditions of the second and third kind, and are wholly obtained by the defunct theory of series. These solutions are also obtained for linear partial differential equations of the second order. They do not apply to solutions of partial differential equations of the first order and they are incapable of solving nonlinear boundary value problems. Analytical Solution Methods for Boundary Value Problems attempts to resolve this issue, using quasi-linearization methods, operational calculus and spatial variable splitting to identify the exact and approximate analytical solutions of three-dimensional non-linear partial differential equations of the first and second order. The work does so uniquely using all analytical formulas for solving equations of mathematical physics without using the theory of series. Within this work, pertinent solutions of linear and nonlinear boundary problems are stated. On the basis of quasi-linearization, operational calculation and splitting on spatial variables, the exact and approached analytical solutions of the equations are obtained in private derivatives of the first and second order. Conditions of unequivocal resolvability of a nonlinear boundary problem are found and the estimation of speed of convergence of iterative process is given. On an example of trial functions results of comparison of the analytical solution are given which have been obtained on suggested mathematical technology, with the exact solution of boundary problems and with the numerical solutions on well-known methods. Discusses the theory and analytical methods for many differential equations appropriate for applied and computational mechanics researchers Addresses pertinent boundary problems in mathematical physics achieved without using the theory of series Includes results that can be used to address nonlinear equations in heat conductivity for the solution of conjugate heat transfer problems and the equations of telegraph and nonlinear transport equation Covers select method solutions for applied mathematicians interested in transport equations methods and thermal protection studies Features extensive revisions from the Russian original, with 115+ new pages of new textual content
Quasilinearization and the Identification Problem
Author: Richard Bellman
Publisher: World Scientific
Published: 1983-08-01
Total Pages: 260
ISBN-13: 9814635650
DOWNLOAD EBOOK →This volume presents an overview of the techniques of quasilinearization as they are applied to the problem of system identification. The quasilinear technique has inherent advantages in establishing the intricate interrelationships which exist in complex physical systems. Several advanced topics which are central to the quasilinear technique are discussed in this book. Problems on orbit determination, estimation of chemical rate constants, complex biomechanics of systems and analytical medicine are investigated, to demonstrate the power of the quasilinear method. The reader will have a good idea of the wide range and complexity of problems which can be solved. Contents:Mathematical ModellingQuasilinearizationOrbit DeterminationEstimation of Chemical Rate ConstantsInverse Problems in EcologyInduced Enzyme SynthesisDistributed SystemsHidden PeriodicitiesMeasurement of Hear ParametersDynamic Programming and an Inverse Problem in Transport TheoryAn Inverse Problem in Mathematical PhysicsThe Identification of Systems with Partial InformationStructural IdentifiabilityFinding an Initial ApproximationDetermining a CriterionSums of ExponentialsFinding Two Defective CoinsThe Motion of a Rocket in a Smoothbore Launcher Readership: Researchers and professionals interested in quasilinear technique and its applications to identification problems and modeling.
Nonlinear Interpolation and Boundary Value Problems
Author: Paul W. Eloe
Publisher: World Scientific
Published: 2016
Total Pages: 249
ISBN-13: 9814733482
DOWNLOAD EBOOK →"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"--
Two-Point Boundary Value Problems: Lower and Upper Solutions
Author: C. De Coster
Publisher: Elsevier
Published: 2006-03-21
Total Pages: 502
ISBN-13: 0080462472
DOWNLOAD EBOOK →This book introduces the method of lower and upper solutions for ordinary differential equations. This method is known to be both easy and powerful to solve second order boundary value problems. Besides an extensive introduction to the method, the first half of the book describes some recent and more involved results on this subject. These concern the combined use of the method with degree theory, with variational methods and positive operators. The second half of the book concerns applications. This part exemplifies the method and provides the reader with a fairly large introduction to the problematic of boundary value problems. Although the book concerns mainly ordinary differential equations, some attention is given to other settings such as partial differential equations or functional differential equations. A detailed history of the problem is described in the introduction. · Presents the fundamental features of the method· Construction of lower and upper solutions in problems· Working applications and illustrated theorems by examples· Description of the history of the method and Bibliographical notes
Quasilinearization and Invariant Imbedding
Author: E. Stanley Lee
Publisher: Elsevier
Published: 2016-06-04
Total Pages: 350
ISBN-13: 1483266753
DOWNLOAD EBOOK →Mathematics in Science and Engineering, Volume 41: Quasilinearization and Invariant Imbedding presents a study on the use of two concepts for obtaining numerical solutions of boundary-value problems—quasilinearization and invariant imbedding. This book emphasizes that the invariant imbedding approach reformulates the original boundary-value problem into an initial value problem by introducing new variables or parameters, while the quasilinearization technique represents an iterative approach combined with linear approximations. This volume focuses on analytical aspects that are concerned with actual convergence rates and computational requirements, considering various efficient algorithms that are suited for various types of boundary-value problems. This publication is a good reference for chemical and control engineers and scientists interested in obtaining numerical solutions of boundary-value problems in their particular fields.
