# Analytical Solution Methods for Boundary Value Problems

Written By • Release : 13 August 2016
• ISBN : 0128043636
• Pages : 200 pages
• Rating : 4/5 from 21 reviews

Read or download book entitled Analytical Solution Methods for Boundary Value Problems written by A.S. Yakimov which was release on 13 August 2016, this book published by Academic Press. Available in PDF, EPUB and Kindle Format. Book excerpt: 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
• Total pages : 200
• ISBN : 0128043636

Summary : 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 ...

## Boundary Value Problems for Engineers • Author : Ali Ümit Keskin
• Publisher : Springer
• Release Date : 2019-06-19
• Total pages : 517
• ISBN : 0128043636

Summary : 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 ...

## Analytical Solutions for Two Ferromagnetic Nanoparticles Immersed in a Magnetic Field • Author : Gehan Anthonys
• Publisher : Morgan & Claypool Publishers
• Release Date : 2018-02-01
• Total pages : 118
• ISBN : 0128043636

Summary : 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 ...

## An Introduction to Continuum Mechanics • Author : J. N. Reddy
• Publisher : Cambridge University Press
• Release Date : 2013-07-29
• Total pages : 212
• ISBN : 0128043636

Summary : 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. ...

## Partial Differential Equations with Fourier Series and Boundary Value Problems • Author : Nakhle H. Asmar
• Publisher : Courier Dover Publications
• Release Date : 2017-03-23
• Total pages : 816
• ISBN : 0128043636

Summary : 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
• Total pages : 474
• ISBN : 0128043636

Summary : 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 ...

## Numerical Solutions of Boundary Value Problems with Finite Difference Method • Author : Sujaul Chowdhury,Ponkog Kumar Das,Syed Badiuzzaman Faruque
• Publisher : Morgan & Claypool Publishers
• Release Date : 2018-09-11
• Total pages : 86
• ISBN : 0128043636

Summary : This book contains an extensive illustration of use of finite difference method in solving the boundary value problem numerically. A wide class of differential equations has been numerically solved in this book. Starting with differential equations of elementary functions like hyperbolic, sine and cosine, we have solved those of special ...

## Boundary Value Problems of Heat Conduction • Author : M. Necati Ozisik
• Publisher : Courier Corporation
• Release Date : 2013-11-26
• Total pages : 512
• ISBN : 0128043636

Summary : Intended for first-year graduate courses in heat transfer, this volume includes topics relevant to chemical and nuclear engineering and aerospace engineering. The systematic and comprehensive treatment employs modern mathematical methods of solving problems in heat conduction and diffusion. Starting with precise coverage of heat flux as a vector, derivation of ...

## Solving Ordinary and Partial Boundary Value Problems in Science and Engineering • Author : Karel Rektorys
• Publisher : CRC Press
• Release Date : 1998-10-20
• Total pages : 224
• ISBN : 0128043636

Summary : 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 ...

## Modeling and Analysis of Chemical Engineering Processes • Author : K. Balu,K. Padmanabhan
• Publisher : I. K. International Pvt Ltd
• Release Date : 2007-01-01
• Total pages : 420
• ISBN : 0128043636

Summary : 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; ...

## Analytical Methods in Marine Hydrodynamics • Author : Ioannis K. Chatjigeorgiou
• Publisher : Cambridge University Press
• Release Date : 2018-05-31
• Total pages : 212
• ISBN : 0128043636

Summary : The value of analytical solutions relies on the rigorous formulation, and a strong mathematical background. This comprehensive volume unifies the most important geometries, which allow for the development of analytical solutions for hydrodynamic boundary value problems. It offers detailed explanations of the Laplance domain and numerical results associated with such ...

## The Finite Element Method for Boundary Value Problems • Author : Karan S. Surana,J. N. Reddy
• Publisher : CRC Press
• Release Date : 2016-11-17
• Total pages : 824
• ISBN : 0128043636

Summary : Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are mathematically classified as ...

## Numerical Solution of Nonlinear Boundary Value Problems with Applications • Author : Milan Kubicek,Vladimir Hlavacek
• Publisher : Courier Corporation
• Release Date : 2008-02
• Total pages : 323
• ISBN : 0128043636

Summary : 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, ...

## Computational Methods in Chemical Engineering with Maple • Author : Ralph E. White,Venkat R. Subramanian
• Publisher : Springer Science & Business Media
• Release Date : 2010-02-06
• Total pages : 860
• ISBN : 0128043636

Summary : This book presents Maple solutions to a wide range of problems relevant to chemical engineers and others. Many of these solutions use Maple’s symbolic capability to help bridge the gap between analytical and numerical solutions. The readers are strongly encouraged to refer to the references included in the book ...

## Solving Nonlinear Boundary Value Problems Using the Homotopy Analysis Method • Author : Ghada Ayed Janem
• Publisher : Unknown
• Release Date : 2015
• Total pages : 148
• ISBN : 0128043636

Summary : Analytical solutions of differential equations are very important for all researchers from different discipline. Obtaining such solutions is difficult in most cases, especially if the differential equation is nonlinear. One of the mostly used methods are the series methods, where the solution is represented as an infinite series. Different methods ...