 ## Analytical Solution Methods for Boundary Value Problems

• Author : A.S. Yakimov
• Release Date : 2016-08-13
• Genre: Mathematics
• Pages : 200
• ISBN 10 : 9780128043639

Analytical Solution Methods for Boundary Value Problems 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 fo ## Numerical analytic Methods in the Theory of Boundary value Problems

• Author : Nikola? Iosifovich Ronto
• Publisher : World Scientific
• Release Date : 2000
• Genre: Mathematics
• Pages : 470
• ISBN 10 : 981023676X

Numerical analytic Methods in the Theory of Boundary value Problems Excerpt :

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 the classical Cesari, Cesari-Hale and Lyapunov-Schmidt methods. ## Numerical Methods for Chemical Engineering

• Author : Kenneth J Beers
• Publisher : Cambridge University Press
• Release Date : 2007
• Genre: Juvenile Nonfiction
• Pages : 496
• ISBN 10 : 0521859719

Numerical Methods for Chemical Engineering Excerpt :

Applications of numerical mathematics and scientific computing to chemical engineering. ## Analytical Solutions for Two Ferromagnetic Nanoparticles Immersed in a Magnetic Field

• Author : Gehan Anthonys
• Publisher : Springer Nature
• Release Date : 2022-06-01
• Genre: Technology & Engineering
• Pages : 102
• ISBN 10 : 9783031020193

Analytical Solutions for Two Ferromagnetic Nanoparticles Immersed in a Magnetic Field Excerpt :

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 a boundary value problem. While there are a vast number of common numerical and analytical methods for solving boundary value problems in the literature, the rapidly growing complexity of these solutions causes increase usage of the computer tools in practical cases. We analytically solve the boundary value problem by using a special technique called a bispherical coordinates system and the numerical computations were obtained by a computer tool. In addition to these details, we will present step-by-step instructions with simple explanations throughout the book, in an effort to act as inspiration in the reader's own modeling for relevant applications in science and engineering. On the other hand, the resulting analytical expressions will constitute benchmark solutions for specified geometric arrangements, which are beneficial for determining the validity of other relevant numerical techniques. The generated results are analyzed quantitatively as well as qualitatively in various approaches. Moreover, the methodology of this book can be adopted for real-world applications in the fields of ferrohydrodynamics, applied electromagnetics, fluid dynamics, electrical engineering, and so forth. Higher-level university students, academics, engineers, scientists, and researchers involved in the aforementioned fields are the intended audience for this book. ## A Course in Differential Equations with Boundary Value Problems

• Author : Stephen A. Wirkus
• Publisher : CRC Press
• Release Date : 2017-01-24
• Genre: Mathematics
• Pages : 708
• ISBN 10 : 9781498736084

A Course in Differential Equations with Boundary Value Problems Excerpt :

A Course in Differential Equations with Boundary Value Problems, 2nd Edition adds additional content to the author’s successful A Course on Ordinary Differential Equations, 2nd Edition. This text addresses the need when the course is expanded. The focus of the text is on applications and methods of solution, both analytical and numerical, with emphasis on methods used in the typical engineering, physics, or mathematics student’s field of study. The text provides sufficient problems so that even the pure math major will be sufficiently challenged. The authors offer a very flexible text to meet a variety of approaches, including a traditional course on the topic. The text can be used in courses when partial differential equations replaces Laplace transforms. There is sufficient linear algebra in the text so that it can be used for a course that combines differential equations and linear algebra. Most significantly, computer labs are given in MATLAB®, Mathematica®, and MapleTM. The book may be used for a course to introduce and equip the student with a knowledge of the given software. Sample course outlines are included. Features MATLAB®, Mathematica®, and MapleTM are incorporated at the end of each chapter. All three software packages have parallel code and exercises; There are numerous problems of varying difficulty for both the applied and pure math major, as well as problems for engineering, physical science and other students. An appendix that gives the reader a "crash course" in the three software packages. Chapter reviews at the end of each chapter to help the students review Projects at the end of each chapter that go into detail about certain topics and introduce new topics that the students are now ready to see Answers to most of the odd problems in the back of the book ## Solving Ordinary and Partial Boundary Value Problems in Science and Engineering

• Author : Karel Rektorys
• Publisher : CRC Press
• Release Date : 1998-10-20
• Genre: Mathematics
• Pages : 218
• ISBN 10 : 0849325528

Solving Ordinary and Partial Boundary Value Problems in Science and Engineering Excerpt :

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 the possibility of generalizations of obtained results and showing connections between them. For the non-mathematician, the author provides profound functional-analytical results without proofs and refers the reader to the literature when necessary. Solving Ordinary and Partial Boundary Value Problems in Science and Engineering contains essential functional analytical concepts, explaining its subject without excessive abstraction. ## A First Course in Integral Equations

• Author : Abdul-Majid Wazwaz
• Publisher : World Scientific Publishing Company
• Release Date : 2015-05-04
• Genre: Mathematics
• Pages : 328
• ISBN 10 : 9789814675147

A First Course in Integral Equations Excerpt :

This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations. It provides a comprehensive treatment of linear and nonlinear Fredholm and Volterra integral equations of the first and second kinds. The materials are presented in an accessible and straightforward manner to readers, particularly those from non-mathematics backgrounds. Numerous well-explained applications and examples as well as practical exercises are presented to guide readers through the text. Selected applications from mathematics, science and engineering are investigated by using the newly developed methods. This volume consists of nine chapters, pedagogically organized, with six chapters devoted to linear integral equations, two chapters on nonlinear integral equations, and the last chapter on applications. It is intended for scholars and researchers, and can be used for advanced undergraduate and graduate students in applied mathematics, science and engineering. Click here for solutions manual. ## An Introduction to Continuum Mechanics

• Author : J. N. Reddy
• Publisher : Cambridge University Press
• Release Date : 2013-07-29
• Genre: Science
• Pages : null
• ISBN 10 : 9781107292406

An Introduction to Continuum Mechanics Excerpt :

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 will pursue further work in fluid dynamics, elasticity, plates and shells, viscoelasticity, plasticity, and interdisciplinary areas such as geomechanics, biomechanics, mechanobiology and nanoscience. The book features derivations of the basic equations of mechanics in invariant (vector and tensor) form and specification of the governing equations to various co-ordinate systems, and numerous illustrative examples, chapter summaries and exercise problems. This second edition includes additional explanations, examples and problems. ## Numerical Solutions of Boundary Value Problems of Non linear Differential Equations

• Author : Sujaul Chowdhury
• Publisher : CRC Press
• Release Date : 2021-10-25
• Genre: Mathematics
• Pages : 112
• ISBN 10 : 9781000486117

Numerical Solutions of Boundary Value Problems of Non linear Differential Equations Excerpt :

The book presents in comprehensive detail numerical solutions to boundary value problems of a number of non-linear differential equations. Replacing derivatives by finite difference approximations in these differential equations leads to a system of non-linear algebraic equations which we have solved using Newton’s iterative method. In each case, we have also obtained Euler solutions and ascertained that the iterations converge to Euler solutions. We find that, except for the boundary values, initial values of the 1st iteration need not be anything close to the final convergent values of the numerical solution. Programs in Mathematica 6.0 were written to obtain the numerical solutions. ## Numerical Solutions of Boundary Value Problems with Finite Difference Method

• Author : Sujaul Chowdhury
• Publisher : Morgan & Claypool
• Release Date : 2018-09-05
• Genre: Science
• Pages : 88
• ISBN 10 : 1643272829

Numerical Solutions of Boundary Value Problems with Finite Difference Method Excerpt :

Containing an extensive illustration of the use of finite difference method in solving boundary value problem numerically, a wide class of differential equations have been numerically solved in this book. ## The Fast Solution of Boundary Integral Equations

• Author : Sergej Rjasanow
• Publisher : Springer Science & Business Media
• Release Date : 2007-04-17
• Genre: Mathematics
• Pages : 284
• ISBN 10 : 9780387340425

The Fast Solution of Boundary Integral Equations Excerpt :

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 Adaptive Cross Approximation Algorithm, starting from the basic ideas and proceeding to their practical realization. Numerous examples representing standard problems are given. ## Partial Differential Equations with Fourier Series and Boundary Value Problems

• Author : Nakhle H. Asmar
• Publisher : Courier Dover Publications
• Release Date : 2017-03-23
• Genre: Mathematics
• Pages : 816
• ISBN 10 : 9780486820835

Partial Differential Equations with Fourier Series and Boundary Value Problems Excerpt :

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. ## Partial Differential Equations and Boundary Value Problems with Applications

• Author : Mark A. Pinsky
• Publisher : American Mathematical Soc.
• Release Date : 2011
• Genre: Mathematics
• Pages : 545
• ISBN 10 : 9780821868898

Partial Differential Equations and Boundary Value Problems with Applications Excerpt :

Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations. ## Analogues for the Solution of Boundary Value Problems

• Author : B. A. Volynskii
• Publisher : Elsevier
• Release Date : 2014-05-17
• Genre: Mathematics
• Pages : 474
• ISBN 10 : 9781483181370

Analogues for the Solution of Boundary Value Problems Excerpt :

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 of electrical simulation and principles involved in the construction of analogues is elaborated in Chapter IV, while the measurements in electrical analogues is deliberated in Chapter V. Chapters VI to VIII describe the construction of network analyzers and star-integrating networks. The methods of physical simulation for the solution of certain boundary-value problems are analyzed in Chapter IX. Chapters X and XI are devoted to future improvements and developments in analogues for the solution of boundary-value problems. This publication is intended for college students and specialists engaged in solving boundary-value problems. ## Boundary Value Problems for Differential Equations

• Author : V. P. Mikhailov
• Publisher : American Mathematical Soc.
• Release Date : 1975
• Genre: Mathematics
• Pages : 266
• ISBN 10 : 0821830260

Boundary Value Problems for Differential Equations Excerpt :