Analytical Solution Methods for Boundary Value Problems

Written By A.S. Yakimov
Analytical Solution Methods for Boundary Value Problems
  • Publsiher : Academic Press
  • Release : 13 August 2016
  • ISBN : 0128043636
  • Pages : 200 pages
  • Rating : 4/5 from 21 reviews
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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

Analytical Solution Methods for Boundary Value Problems
  • Author : A.S. Yakimov
  • Publisher : Academic Press
  • Release Date : 2016-08-13
  • Total pages : 200
  • ISBN : 0128043636
GET BOOK

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 ...

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 Date : 2000-06-30
  • Total pages : 468
  • ISBN : 0128043636
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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 ...

Spline Solutions of Higher Order Boundary Value Problems

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

Solving Ordinary and Partial Boundary Value Problems in Science and Engineering

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
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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 ...

Numerical Solution of Two Point Boundary Value Problems

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

Finite Difference Methods Theory and Applications

Finite Difference Methods  Theory and Applications
  • Author : Ivan Dimov,István Faragó,Lubin Vulkov
  • Publisher : Springer
  • Release Date : 2019-01-28
  • Total pages : 688
  • ISBN : 0128043636
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Summary : 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 ...

Iterative Methods for the Numerical Solutions of Boundary Value Problems

Iterative Methods for the Numerical Solutions of Boundary Value Problems
  • Author : Mariam B. H. Abushammala
  • Publisher : Unknown
  • Release Date : 2014
  • Total pages : 208
  • ISBN : 0128043636
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Summary : "The aim of this thesis is twofold. First of all, in Chapters 1 and 2, we review the well-known Adomian Decomposition Method (ADM) and Variational Iteration Method (VIM) for obtaining exact and numerical solutions for ordinary differential equations, partial differential equations, integral equations, integro-differential equations, delay differential equations, and algebraic equations in ...

Nonlinear Ordinary Differential Equations

Nonlinear Ordinary Differential Equations
  • Author : Martin Hermann,Masoud Saravi
  • Publisher : Springer
  • Release Date : 2016-05-09
  • Total pages : 310
  • ISBN : 0128043636
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Summary : The book discusses the solutions to nonlinear ordinary differential equations (ODEs) using analytical and numerical approximation methods. Recently, analytical approximation methods have been largely used in solving linear and nonlinear lower-order ODEs. It also discusses using these methods to solve some strong nonlinear ODEs. There are two chapters devoted to ...

Electromagnetic Wave Theory for Boundary Value Problems

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
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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 ...

Hodge Decomposition A Method for Solving Boundary Value Problems

Hodge Decomposition   A Method for Solving Boundary Value Problems
  • Author : Günter Schwarz
  • Publisher : Springer
  • Release Date : 2006-11-14
  • Total pages : 164
  • ISBN : 0128043636
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Summary : Hodge theory is a standard tool in characterizing differ- ential complexes and the topology of manifolds. This book is a study of the Hodge-Kodaira and related decompositions on manifolds with boundary under mainly analytic aspects. It aims at developing a method for solving boundary value problems. Analysing a Dirichlet form ...

Boundary Value Problems for Analytic Functions

Boundary Value Problems for Analytic Functions
  • Author : Jian-Ke Lu
  • Publisher : World Scientific
  • Release Date : 1993
  • Total pages : 466
  • ISBN : 0128043636
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Summary : 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, ...

Advanced Engineering Mathematics with Mathematica

Advanced Engineering Mathematics with Mathematica
  • Author : Edward B. Magrab
  • Publisher : CRC Press
  • Release Date : 2020-02-26
  • Total pages : 529
  • ISBN : 0128043636
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Summary : Advanced Engineering Mathematics with Mathematica® presents advanced analytical solution methods that are used to solve boundary-value problems in engineering and integrates these methods with Mathematica® procedures. It emphasizes the Sturm–Liouville system and the generation and application of orthogonal functions, which are used by the separation of variables method to ...

Analytical and Numerical Methods for Convection dominated and Singularly Perturbed Problems

Analytical and Numerical Methods for Convection dominated and Singularly Perturbed Problems
  • Author : Lubin Vulkov,John J. H. Miller,G. I. Shishkin
  • Publisher : Nova Publishers
  • Release Date : 2000
  • Total pages : 277
  • ISBN : 0128043636
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Summary : The proceedings of the Workshop on Analytical and Computational Methods for Convention-Dominated and Singularly Peturbed Problems, Lozenetz, Bulgaria, 27-31 August, 1998. The volume includes 13 lectures and 19 papers presented at the workshop, providing an overview of developments in the theory and applications of advanced numerical methods to problems having boundary and interior ...

Differential Equations with Boundary Value Problems

Differential Equations with Boundary Value Problems
  • Author : Dennis G. Zill
  • Publisher : Cengage Learning
  • Release Date : 2016-12-05
  • Total pages : 664
  • ISBN : 0128043636
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Summary : DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 9th Edition, strikes a balance between the analytical, qualitative, and quantitative approaches to the study of Differential Equations. This proven text speaks to students of varied majors through a wealth of pedagogical aids, including an abundance of examples, explanations, Remarks boxes, and definitions. Written in ...

Numerical Methods for Elliptic Problems with Singularities

Numerical Methods for Elliptic Problems with Singularities
  • Author : Zi-Cai Li
  • Publisher : World Scientific
  • Release Date : 1990
  • Total pages : 258
  • ISBN : 0128043636
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Summary : This book presents two kinds of numerical methods for solving elliptic boundary value problems with singularities. Part I gives the boundary methods which use analytic and singular expansions, and Part II the nonconforming methods combining finite element methods (FEM) (or finite difference methods (FDM)) and singular (or analytic) expansions. The ...