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

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  • Author : A.S. Yakimov
  • Publisher : Academic Press
  • Pages : 200 pages
  • ISBN : 0128043636
  • Rating : 4/5 from 21 reviews
CLICK HERE TO GET THIS BOOKAnalytical Solution Methods for Boundary Value Problems

Analytical Solution Methods for Boundary Value Problems

Analytical Solution Methods for Boundary Value Problems
  • Author : A.S. Yakimov
  • Publisher : Academic Press
  • Release : 13 August 2016
GET THIS BOOKAnalytical 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

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  • Author : Gehan Anthonys
  • Publisher : Morgan & Claypool Publishers
  • Release : 01 February 2018
GET THIS BOOKAnalytical Solutions for Two Ferromagnetic Nanoparticles Immersed in a Magnetic Field

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

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  • Publisher : Springer Science & Business
  • Release : 22 April 2014
GET THIS BOOKA First Course in Ordinary Differential Equations

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

Numerical-Analytic Methods in the Theory of Boundary-Value Problems

Numerical-Analytic Methods in the Theory of Boundary-Value Problems
  • Author : M Ronto,A M Samoilenko
  • Publisher : World Scientific
  • Release : 30 June 2000
GET THIS BOOKNumerical-Analytic Methods in the Theory of Boundary-Value Problems

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

A Unified Approach to Boundary Value Problems

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  • Author : Athanassios S. Fokas
  • Publisher : SIAM
  • Release : 06 November 2008
GET THIS BOOKA Unified Approach to Boundary Value Problems

A novel approach to analysing initial-boundary value problems for integrable partial differential equations (PDEs) in two dimensions, based on ideas of the inverse scattering transform that the author introduced in 1997. This method is unique in also yielding novel integral representations for linear PDEs. Several new developments are addressed in the book, including a new transform method for linear evolution equations on the half-line and on the finite interval; analytical inversion of certain integrals such as the attenuated Radon transform and

Extrema of Nonlocal Functionals and Boundary Value Problems for Functional Differential Equations

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  • Author : Georgiĭ Aleksandrovich Kamenskiĭ
  • Publisher : Nova Publishers
  • Release : 28 October 2021
GET THIS BOOKExtrema of Nonlocal Functionals and Boundary Value Problems for Functional Differential Equations

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 equations. The book is dedicated to systematic study of variational calculus for non-local functionals and to theory of boundary value problems for functional differential equations. There are described different necessary

Solving Ordinary and Partial Boundary Value Problems in Science and Engineering

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

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 Analytic Functions

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  • Author : Jian-Ke Lu
  • Publisher : World Scientific
  • Release : 28 October 1993
GET THIS BOOKBoundary Value Problems for Analytic Functions

This book deals with boundary value problems for analytic functions with applications to singular integral equations. New and simpler proofs of certain classical results such as the Plemelj formula, the Privalov theorem and the Poincar‚-Bertrand formula are given. Nearly one third of this book contains the author's original works, most of which have not been published in English before and, hence, were previously unknown to most readers in the world.It consists of 7 chapters together with an appendix: Chapter

Numerical-analytic Methods in the Theory of Boundary-value Problems

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  • Author : Nikola? Iosifovich Ronto,Anatoli? Mikha?lovich Samo?lenko
  • Publisher : World Scientific
  • Release : 28 October 2021
GET THIS BOOKNumerical-analytic Methods in the Theory of Boundary-value Problems

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

Boundary Value Problems

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  • Author : F. D. Gakhov
  • Publisher : Elsevier
  • Release : 10 July 2014
GET THIS BOOKBoundary Value Problems

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

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  • Author : Michael T. Heath
  • Publisher : SIAM
  • Release : 14 November 2018
GET THIS BOOKScientific Computing

This book differs from traditional numerical analysis texts in that it focuses on the motivation and ideas behind the algorithms presented rather than on detailed analyses of them. It presents a broad overview of methods and software for solving mathematical problems arising in computational modeling and data analysis, including proper problem formulation, selection of effective solution algorithms, and interpretation of results.? In the 20 years since its original publication, the modern, fundamental perspective of this book has aged well, and it

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  • Author : Ali Ümit Keskin
  • Publisher : Springer
  • Release : 19 June 2019
GET THIS BOOKBoundary Value Problems for Engineers

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

Analogues for the Solution of Boundary-Value Problems

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  • Author : B. A. Volynskii,V. Ye. Bukhman
  • Publisher : Elsevier
  • Release : 17 May 2014
GET THIS BOOKAnalogues for the Solution of Boundary-Value Problems

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