# Analytical Solution Methods for Boundary Value Problems

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

Produk Detail:

• Author : A.S. Yakimov
• Pages : 200 pages
• ISBN : 0128043636
• Rating : 4/5 from 21 reviews

## Analytical Solution Methods for Boundary Value Problems • Author : A.S. Yakimov
• Release : 13 August 2016

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

## Solving Ordinary and Partial Boundary Value Problems in Science and Engineering • Author : Karel Rektorys
• Publisher : CRC Press
• Release : 20 October 1998

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

## Boundary Value Problems for Engineers • Author : Ali Ümit Keskin
• Publisher : Springer
• Release : 19 June 2019

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

## Numerical-analytic Methods in the Theory of Boundary-value Problems • Author : Nikola? Iosifovich Ronto,Anatoli? Mikha?lovich Samo?lenko
• Publisher : World Scientific
• Release : 21 January 2021

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 : Morgan & Claypool Publishers
• Release : 01 February 2018

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

## An Introduction to Continuum Mechanics • Author : J. N. Reddy
• Publisher : Cambridge University Press
• Release : 29 July 2013

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 Solution of Two Point Boundary Value Problems • Author : Herbert B. Keller
• Publisher : SIAM
• Release : 21 January 1976

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.

## Boundary Value Problems of Heat Conduction • Author : M. Necati Ozisik
• Publisher : Courier Corporation
• Release : 01 January 2002

Intended for first-year graduate courses in heat transfer, including topics relevant to aerospace engineering and chemical and nuclear engineering, this hardcover book deals systematically and comprehensively with modern mathematical methods of solving problems in heat conduction and diffusion. Includes illustrative examples and problems, plus helpful appendixes. 134 illustrations. 1968 edition.

## Numerical Solution of Boundary Value Problems for Ordinary Differential Equations • Author : Uri M. Ascher,Robert M. M. Mattheij,Robert D. Russell
• Publisher : SIAM
• Release : 01 December 1994

This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one

## Finite Difference Methods. Theory and Applications • Author : Ivan Dimov,István Faragó,Lubin Vulkov
• Publisher : Springer
• Release : 28 January 2019

This book constitutes the refereed conference proceedings of the 7th International Conference on Finite Difference Methods, FDM 2018, held in Lozenetz, Bulgaria, in June 2018.The 69 revised full papers presented together with 11 invited papers were carefully reviewed and selected from 94 submissions. They deal with many modern and new numerical techniques like splitting techniques, Green’s function method, multigrid methods, and immersed interface method.

## Fourier Series and Numerical Methods for Partial Differential Equations • Author : Richard Bernatz
• Publisher : John Wiley & Sons
• Release : 30 July 2010

The importance of partial differential equations (PDEs) in modeling phenomena in engineering as well as in the physical, natural, and social sciences is well known by students and practitioners in these fields. Striking a balance between theory and applications, Fourier Series and Numerical Methods for Partial Differential Equations presents an introduction to the analytical and numerical methods that are essential for working with partial differential equations. Combining methodologies from calculus, introductory linear algebra, and ordinary differential equations (ODEs), the book

## Unified Transform for Boundary Value Problems • Author : Athanasios S. Fokas,Beatrice Pelloni
• Publisher : SIAM
• Release : 01 January 2015

This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for

## Boundary Value Problems for Partial Differential Equations and Applications in Electrodynamics • Author : N E Tovmasyan
• Publisher : World Scientific
• Release : 08 February 1994

The book is devoted to boundary value problems for general partial differential equations. Efficient methods of resolution of boundary value problems for elliptic equations, based on the theory of analytic functions and having great theoretical and practical importance are developed. A new approach to the investigation of electromagnetic fields is sketched, permitting laws of propagation of electromagnetic energy at a great distance, is outlined and asymptotic formulae for solutions of Maxwell's equation is obtained. These equations are also applied to

## A First Course in Ordinary Differential Equations • Author : Martin Hermann,Masoud Saravi
• Publisher : Springer Science & Business
• Release : 22 April 2014

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 level, to introduce and study the mathematics of ODEs. The analytical part of the book deals with solution techniques for scalar first-order and second-order linear ODEs, and systems of linear

## Boundary Value Problems • Author : F. D. Gakhov
• Publisher : Elsevier
• Release : 10 July 2014

Boundary Value Problems is a translation from the Russian of lectures given at Kazan and Rostov Universities, dealing with the theory of boundary value problems for analytic functions. The emphasis of the book is on the solution of singular integral equations with Cauchy and Hilbert kernels. Although the book treats the theory of boundary value problems, emphasis is on linear problems with one unknown function. The definition of the Cauchy type integral, examples, limiting values, behavior, and its principal value