# 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 ...

## Spline Solutions of Higher Order Boundary Value Problems • Author : Parcha Kalyani
• Publisher : GRIN Verlag
• Release Date : 2020-06-09
• Total pages : 122
• ISBN : 0128043636

Summary : 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 ...

## 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 ...

## Numerical Analytic Methods in the Theory of Boundary Value Problems • Author : M Ronto,A M Samoilenko
• Publisher : World Scientific
• Release Date : 2000-06-30
• Total pages : 468
• ISBN : 0128043636

Summary : 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 ...

## Numerical Solution of Two Point Boundary Value Problems • Author : Herbert B. Keller
• Publisher : SIAM
• Release Date : 1976
• Total pages : 59
• ISBN : 0128043636

Summary : 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....

## 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 ...

## Electromagnetic Wave Theory for Boundary Value Problems • Author : Hyo J. Eom
• Publisher : Springer Science & Business Media
• Release Date : 2013-06-29
• Total pages : 314
• ISBN : 0128043636

Summary : Electromagnetic wave theory is based on Maxwell's equations, and electromagnetic boundary-value problems must be solved to understand electromagnetic scattering, propagation, and radiation. Electromagnetic theory finds practical applications in wireless telecommunications and microwave engineering. This book is written as a text for a two-semester graduate course on electromagnetic wave theory. As ...

## Advanced Numerical and Semi Analytical Methods for Differential Equations • Author : Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
• Publisher : John Wiley & Sons
• Release Date : 2019-04-10
• Total pages : 256
• ISBN : 0128043636

Summary : Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional ...

## A First Course in Ordinary Differential Equations • Author : Martin Hermann,Masoud Saravi
• Publisher : Springer Science & Business
• Release Date : 2014-04-22
• Total pages : 288
• ISBN : 0128043636

Summary : This book presents a modern introduction to analytical and numerical techniques for solving ordinary differential equations (ODEs). Contrary to the traditional format—the theorem-and-proof format—the book is focusing on analytical and numerical methods. The book supplies a variety of problems and examples, ranging from the elementary to the advanced ...

## The Fast Solution of Boundary Integral Equations • Author : Sergej Rjasanow,Olaf Steinbach
• Publisher : Springer Science & Business Media
• Release Date : 2007-04-17
• Total pages : 284
• ISBN : 0128043636

Summary : 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 ...

## Extrema of Nonlocal Functionals and Boundary Value Problems for Functional Differential Equations • Author : Georgiĭ Aleksandrovich Kamenskiĭ
• Publisher : Nova Publishers
• Release Date : 2007
• Total pages : 225
• ISBN : 0128043636

Summary : The non-local functional is an integral with the integrand depending on the unknown function at different values of the argument. These types of functionals have different applications in physics, engineering and sciences. The Euler type equations that arise as necessary conditions of extrema of non-local functionals are the functional differential ...

## 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 ...

## 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
• Total pages : 455
• ISBN : 0128043636

Summary : 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 ...

## Differential Equation Solutions with MATLAB • Author : Dingyü Xue
• Publisher : Walter de Gruyter GmbH & Co KG
• Release Date : 2020-04-06
• Total pages : 451
• ISBN : 0128043636

Summary : This book focuses the solutions of differential equations with MATLAB. Analytical solutions of differential equations are explored first, followed by the numerical solutions of different types of ordinary differential equations (ODEs), as well as the universal block diagram based schemes for ODEs. Boundary value ODEs, fractional-order ODEs and partial differential ...

## Numerical Methods in Engineering Science • Author : Graham de Vahl Davis
• Publisher : Springer Science & Business Media
• Release Date : 2012-12-06
• Total pages : 286
• ISBN : 0128043636

Summary : This book is designed for an introductory course in numerical methods for students of engineering and science at universities and colleges of advanced education. It is an outgrowth of a course of lectures and tutorials (problem solving sessions) which the author has given for a number of years at the ...