# Analytical Solution Methods for Boundary Value Problems

• Release : 13 August 2016
• ISBN : 9780128043639
• Page : 200 pages
• Rating : 4.5/5 from 103 voters

## Download Analytical Solution Methods for Boundary Value Problems in PDF, Epub and Kindle

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

### Analytical Solution Methods for Boundary Value Problems • Author : A.S. Yakimov
• Release Date : 2016-08-13
• ISBN : 9780128043639

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

### Numerical-analytic Methods in the Theory of Boundary-value Problems • Author : Nikola? Iosifovich Ronto,Anatoli? Mikha?lovich Samo?lenko
• Publisher : World Scientific
• Release Date : 2000
• ISBN : 981023676X

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

### Analytical Solutions for Two Ferromagnetic Nanoparticles Immersed in a Magnetic Field • Author : Gehan Anthonys
• Publisher : Springer Nature
• Release Date : 2022-06-01
• ISBN : 9783031020193

The investigation of the behavior of ferromagnetic particles in an external magnetic field is important for use in a wide range of applications in magnetostatics problems, from biomedicine to engineering. To the best of the author's knowledge, the systematic analysis for this kind of investigation is not available in the current literature. Therefore, this book contributes a complete solution for investigating the behavior of two ferromagnetic spherical particles, immersed in a uniform magnetic field, by obtaining exact mathematical models on

### A Course in Differential Equations with Boundary Value Problems • Author : Stephen A. Wirkus,Randall J. Swift,Ryan Szypowski
• Publisher : CRC Press
• Release Date : 2017-01-24
• ISBN : 9781498736084

A Course in Differential Equations with Boundary Value Problems, 2nd Edition adds additional content to the author’s successful A Course on Ordinary Differential Equations, 2nd Edition. This text addresses the need when the course is expanded. The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student’s field of study. The text provides sufficient problems so that even the pure

### Solving Ordinary and Partial Boundary Value Problems in Science and Engineering • Author : Karel Rektorys
• Publisher : CRC Press
• Release Date : 1998-10-20
• ISBN : 0849325528

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

### An Introduction to Continuum Mechanics • Author : J. N. Reddy
• Publisher : Cambridge University Press
• Release Date : 2013-07-29
• ISBN : 9781107292406

This best-selling textbook presents the concepts of continuum mechanics in a simple yet rigorous manner. It introduces the invariant form as well as the component form of the basic equations and their applications to problems in elasticity, fluid mechanics and heat transfer, and offers a brief introduction to linear viscoelasticity. The book is ideal for advanced undergraduates and graduate students looking to gain a strong background in the basic principles common to all major engineering fields, and for those who

### Numerical Solutions of Boundary Value Problems of Non-linear Differential Equations • Author : Sujaul Chowdhury,Syed Badiuzzaman Faruque,Ponkog Kumar Das
• Publisher : CRC Press
• Release Date : 2021-10-25
• ISBN : 9781000486117

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

### A First Course in Integral Equations • Author : Abdul-Majid Wazwaz
• Publisher : World Scientific Publishing Company
• Release Date : 2015-05-04
• ISBN : 9789814675147

This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations. It provides a comprehensive treatment of linear and nonlinear Fredholm and Volterra integral equations of the first and second kinds. The materials are presented in an accessible and straightforward manner to readers, particularly those from non-mathematics backgrounds. Numerous well-explained applications and examples as well as practical exercises are presented to guide readers through the text. Selected applications from

### Numerical Solutions of Boundary Value Problems with Finite Difference Method • Author : Sujaul Chowdhury,Ponkog Kumar Das,Syed Badiuzzaman Faruque
• Publisher : Morgan & Claypool
• Release Date : 2018-09-05
• ISBN : 1643272829

Containing an extensive illustration of the use of finite difference method in solving boundary value problem numerically, a wide class of differential equations have been numerically solved in this book.

### Constructive Methods for Linear and Nonlinear Boundary Value Problems for Analytic Functions • Author : v Mityushev,S V Rogosin
• Publisher : CRC Press
• Release Date : 1999-11-29
• ISBN : 1584880570

Constructive methods developed in the framework of analytic functions effectively extend the use of mathematical constructions, both within different branches of mathematics and to other disciplines. This monograph presents some constructive methods-based primarily on original techniques-for boundary value problems, both linear and nonlinear. From among the many applications to which these methods can apply, the authors focus on interesting problems associated with composite materials with a finite number of inclusions. How far can one go in the solutions of problems

### The Fast Solution of Boundary Integral Equations • Author : Sergej Rjasanow,Olaf Steinbach
• Publisher : Springer Science & Business Media
• Release Date : 2007-04-17
• ISBN : 9780387340425

This book provides a detailed description of fast boundary element methods, all based on rigorous mathematical analysis. In particular, the authors use a symmetric formulation of boundary integral equations as well as discussing Galerkin discretisation. All the necessary related stability and error estimates are derived. The authors therefore describe the Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given.

### Partial Differential Equations and Boundary-Value Problems with Applications • Author : Mark A. Pinsky
• Publisher : American Mathematical Soc.
• Release Date : 2011
• ISBN : 9780821868898

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

### Partial Differential Equations with Fourier Series and Boundary Value Problems • Author : Nakhle H. Asmar
• Publisher : Courier Dover Publications
• Release Date : 2017-03-23
• ISBN : 9780486820835

Rich in proofs, examples, and exercises, this widely adopted text emphasizes physics and engineering applications. The Student Solutions Manual can be downloaded free from Dover's site; the Instructor Solutions Manual is available upon request. 2004 edition, with minor revisions.

### Analogues for the Solution of Boundary-Value Problems • Author : B. A. Volynskii,V. Ye. Bukhman
• Publisher : Elsevier
• Release Date : 2014-05-17
• ISBN : 9781483181370

Analogues for the Solution of Boundary-Value Problems considers the simulation of integral methods of solving boundary-value problems. This book is organized into 11 chapters. After the introduction provided in Chapter I, the formulation of some important engineering problems that reduce to the solution of partial differential equations is reviewed in Chapter II. Chapter III covers the mathematical methods for the solution of problems, such as the thermal problem of electrode graphitization and underground coal gasification. The theory of the physical processes

### Modeling and Analysis of Chemical Engineering Processes • Author : K. Balu,K. Padmanabhan
• Publisher : I. K. International Pvt Ltd
• Release Date : 2007
• ISBN : 9788189866310

The chemical process industry faces serious problems with regard to new materials and efficient methods of production due to increasing costs of energy, stringent environmental regulations and global competition. A clear understanding of the processes is required in order to solve these problems. One way is through crisp modeling method; another is through an optimal operation of the process to improve profitability and efficiency. The book is in two parts. The first part discusses the methods of modeling chemical engineering