Solving Ordinary And Partial Boundary Value Problems In Science And Engineering

Author : Karel Rektorys
Publisher : CRC Press
Page : 218 pages
File Size : 41,8 Mb
Release : 1998-10-20
Category : Mathematics
ISBN : 0849325528

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Solving Ordinary and Partial Boundary Value Problems in Science and Engineering by Karel Rektorys Pdf

This book provides an elementary, accessible introduction for engineers and scientists to the concepts of ordinary and partial boundary value problems, acquainting readers with fundamental properties and with efficient methods of constructing solutions or satisfactory approximations. Discussions include: ordinary differential equations classical theory of partial differential equations Laplace and Poisson equations heat equation variational methods of solution of corresponding boundary value problems methods of solution for evolution partial differential equations The author presents special remarks for the mathematical reader, demonstrating the possibility of generalizations of obtained results and showing connections between them. For the non-mathematician, the author provides profound functional-analytical results without proofs and refers the reader to the literature when necessary. Solving Ordinary and Partial Boundary Value Problems in Science and Engineering contains essential functional analytical concepts, explaining its subject without excessive abstraction.

Author : R. Seshadri,T.Y. Na
Publisher : Springer Science & Business Media
Page : 232 pages
File Size : 47,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461251026

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Group Invariance in Engineering Boundary Value Problems by R. Seshadri,T.Y. Na Pdf

REFEREN CES . 156 9 Transforma.tion of a Boundary Value Problem to an Initial Value Problem . 157 9.0 Introduction . 157 9.1 Blasius Equation in Boundary Layer Flow . 157 9.2 Longitudinal Impact of Nonlinear Viscoplastic Rods . 163 9.3 Summary . 168 REFERENCES . . . . . . . . . . . . . . . . . . 168 . 10 From Nonlinear to Linear Differential Equa.tions Using Transformation Groups. . . . . . . . . . . . . . 169 . 10.1 From Nonlinear to Linear Differential Equations . 170 10.2 Application to Ordinary Differential Equations -Bernoulli's Equation . . . . . . . . . . . 173 10.3 Application to Partial Differential Equations -A Nonlinear Chemical Exchange Process . 178 10.4 Limitations of the Inspectional Group Method . 187 10.5 Summary . 188 REFERENCES . . . . 188 11 Miscellaneous Topics . 190 11.1 Reduction of Differential Equations to Algebraic Equations 190 11.2 Reduction of Order of an Ordinary Differential Equation . 191 11.3 Transformat.ion From Ordinary to Partial Differential Equations-Search for First Integrals . . . . . . " 193 . 11.4 Reduction of Number of Variables by Multiparameter Groups of Transformations . . . . . . . . .. . . . 194 11.5 Self-Similar Solutions of the First and Second Kind . . 202 11.6 Normalized Representation and Dimensional Consideration 204 REFERENCES .206 Problems . 208 .220 Index .. Chapter 1 INTRODUCTION AND GENERAL OUTLINE Physical problems in engineering science are often described by dif ferential models either linear or nonlinear. There is also an abundance of transformations of various types that appear in the literature of engineer ing and mathematics that are generally aimed at obtaining some sort of simplification of a differential model.

Author : Stanley J. Farlow
Publisher : Courier Corporation
Page : 414 pages
File Size : 48,5 Mb
Release : 2012-03-08
Category : Mathematics
ISBN : 9780486134734

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Partial Differential Equations for Scientists and Engineers by Stanley J. Farlow Pdf

Practical text shows how to formulate and solve partial differential equations. Coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, numerical and approximate methods. Solution guide available upon request. 1982 edition.

Author : S. Chakraverty,Susmita Mall
Publisher : CRC Press
Page : 156 pages
File Size : 40,6 Mb
Release : 2017-07-20
Category : Mathematics
ISBN : 9781351651318

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Artificial Neural Networks for Engineers and Scientists by S. Chakraverty,Susmita Mall Pdf

Differential equations play a vital role in the fields of engineering and science. Problems in engineering and science can be modeled using ordinary or partial differential equations. Analytical solutions of differential equations may not be obtained easily, so numerical methods have been developed to handle them. Machine intelligence methods, such as Artificial Neural Networks (ANN), are being used to solve differential equations, and these methods are presented in Artificial Neural Networks for Engineers and Scientists: Solving Ordinary Differential Equations. This book shows how computation of differential equation becomes faster once the ANN model is properly developed and applied.

Author : David L. Powers
Publisher : Academic Press
Page : 516 pages
File Size : 51,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9780125637381

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Boundary Value Problems by David L. Powers Pdf

Preface -- Chapter 0. Ordinary Differential Equations -- Chapter 1. Fourier Series and Integrals -- Chapter 2. The Heat Equation -- Chapter 3. The Wave Equation -- Chapter 4. The Potential Equation -- Chapter 5. Higher Dimensions & Other Coordinates.

Author : Ali Ümit Keskin
Publisher : Springer
Page : 517 pages
File Size : 42,8 Mb
Release : 2019-06-19
Category : Technology & Engineering
ISBN : 9783030210809

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Boundary Value Problems for Engineers by Ali Ümit Keskin Pdf

This book is designed to supplement standard texts and teaching material in the areas of differential equations in engineering such as in Electrical ,Mechanical and Biomedical engineering. Emphasis is placed on the Boundary Value Problems that are often met in these fields.This keeps the the spectrum of the book rather focussed .The book has basically emerged from the need in the authors lectures on “Advanced Numerical Methods in Biomedical Engineering” at Yeditepe University and it is aimed to assist the students in solving general and application specific problems in Science and Engineering at upper-undergraduate and graduate level.Majority of the problems given in this book are self-contained and have varying levels of difficulty to encourage the student. Problems that deal with MATLAB simulations are particularly intended to guide the student to understand the nature and demystify theoretical aspects of these problems. Relevant references are included at the end of each chapter. Here one will also find large number of software that supplements this book in the form of MATLAB script (.m files). The name of the files used for the solution of a problem are indicated at the end of each corresponding problem statement.There are also some exercises left to students as homework assignments in the book. An outstanding feature of the book is the large number and variety of the solved problems that are included in it. Some of these problems can be found relatively simple, while others are more challenging and used for research projects. All solutions to the problems and script files included in the book have been tested using recent MATLAB software.The features and the content of this book will be most useful to the students studying in Engineering fields, at different levels of their education (upper undergraduate-graduate).

Author : James M. Hill
Publisher : CRC Press
Page : 232 pages
File Size : 40,5 Mb
Release : 1992-03-17
Category : Mathematics
ISBN : 0849344425

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Differential Equations and Group Methods for Scientists and Engineers by James M. Hill Pdf

Differential Equations and Group Methods for Scientists and Engineers presents a basic introduction to the technically complex area of invariant one-parameter Lie group methods and their use in solving differential equations. The book features discussions on ordinary differential equations (first, second, and higher order) in addition to partial differential equations (linear and nonlinear). Each chapter contains worked examples with several problems at the end; answers to these problems and hints on how to solve them are found at the back of the book. Students and professionals in mathematics, science, and engineering will find this book indispensable for developing a fundamental understanding of how to use invariant one-parameter group methods to solve differential equations.

Author : Parcha Kalyani
Publisher : GRIN Verlag
Page : 122 pages
File Size : 42,6 Mb
Release : 2020-06-09
Category : Mathematics
ISBN : 9783346177995

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Spline Solutions of Higher Order Boundary Value Problems by Parcha Kalyani Pdf

Doctoral Thesis / Dissertation from the year 2014 in the subject Mathematics - Applied Mathematics, , language: English, abstract: Some of the problems of real world phenomena can be described by differential equations involving the ordinary or partial derivatives with some initial or boundary conditions. To interpret the physical behavior of the problem it is necessary to know the solution of the differential equation. Unfortunately, it is not possible to solve some of the differential equations whether they are ordinary or partial with initial or boundary conditions through the analytical methods. When, we fail to find the solution of ordinary differential equation or partial differential equation with initial or boundary conditions through the analytical methods, one can obtain the numerical solution of such problems through the numerical methods up to the desired degree of accuracy. Of course, these numerical methods can also be applied to find the numerical solution of a differential equation which can be solved analytically. Several problems in natural sciences, social sciences, medicine, business management, engineering, particle dynamics, fluid mechanics, elasticity, heat transfer, chemistry, economics, anthropology and finance can be transformed into boundary value problems using mathematical modeling. A few problems in various fields of science and engineering yield linear and nonlinear boundary value problems of second order such as heat equation in thermal studies, wave equation in communication etc. Fifth-order boundary value problems generally arise in mathematical modeling of viscoelastic flows. The dynamo action in some stars may be modeled by sixth-order boundary-value problems. The narrow convecting layers bounded by stable layers which are believed to surround A-type stars may be modeled by sixth-order boundary value problems which arise in astrophysics. The seventh order boundary value problems generally arise in modeling induction motors with two rotor circuits. Various phenomena such as convection, flow in wind tunnels, lee waves, eddies, etc. can also be modeled by higher order boundary value problems.

Author : K. Rektorys
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 51,5 Mb
Release : 1980-02-29
Category : Mathematics
ISBN : 9027710600

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Variational Methods in Mathematics, Science and Engineering by K. Rektorys Pdf

Hilbert space; Variational methods; Application of variational methods to the solution of boundary value problems in ordinary and partial differential equations; Theory of boundary value problems in differential equations based on the concept of a weak solution and on the lax-milgram theorem; The eigenvalue problem; Some special methods. Regularity of the weak solution.

Author : T.Y. Na
Publisher : Academic Press
Page : 321 pages
File Size : 41,8 Mb
Release : 1980-01-18
Category : Computers
ISBN : 9780080956534

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Computational Methods in Engineering Boundary Value Problems by T.Y. Na Pdf

Computational Methods in Engineering Boundary Value Problems

Author : C. De Coster,P. Habets
Publisher : Elsevier
Page : 502 pages
File Size : 55,5 Mb
Release : 2006-03-21
Category : Mathematics
ISBN : 9780080462479

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Two-Point Boundary Value Problems: Lower and Upper Solutions by C. De Coster,P. Habets Pdf

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

Author : Geoffrey Stephenson
Publisher : Longman Publishing Group
Page : 180 pages
File Size : 47,9 Mb
Release : 1985
Category : Mathematics
ISBN : UOM:39015049316238

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Partial Differential Equations for Scientists and Engineers by Geoffrey Stephenson Pdf

Author : Thomas Hillen,I. E. Leonard,Henry van Roessel
Publisher : John Wiley & Sons
Page : 610 pages
File Size : 40,6 Mb
Release : 2014-08-21
Category : Mathematics
ISBN : 9781118438435

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Partial Differential Equations by Thomas Hillen,I. E. Leonard,Henry van Roessel Pdf

Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin by describing functions and their partial derivatives while also defining the concepts of elliptic, parabolic, and hyperbolic PDEs. Following an introduction to basic theory, subsequent chapters explore key topics including: • Classification of second-order linear PDEs • Derivation of heat, wave, and Laplace’s equations • Fourier series • Separation of variables • Sturm-Liouville theory • Fourier transforms Each chapter concludes with summaries that outline key concepts. Readers are provided the opportunity to test their comprehension of the presented material through numerous problems, ranked by their level of complexity, and a related website features supplemental data and resources. Extensively class-tested to ensure an accessible presentation, Partial Differential Equations is an excellent book for engineering, mathematics, and applied science courses on the topic at the upper-undergraduate and graduate levels.

Author : Milan Kubicek,Vladimir Hlavacek
Publisher : Courier Corporation
Page : 338 pages
File Size : 49,6 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 : Mark A. Pinsky
Publisher : American Mathematical Soc.
Page : 545 pages
File Size : 47,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821868898

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Partial Differential Equations and Boundary-Value Problems with Applications by Mark A. Pinsky Pdf

Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.