Analytical Solution Methods for Boundary Value Problems
Analytical Solution Methods for Boundary Value Problems

Author: A.S. Yakimov

Publisher: Academic Press

Published: 2016-08-13

Total Pages: 202

ISBN-13: 0128043636

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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

Applied Numerical Methods with MATLAB for Engineers and Scientists
Applied Numerical Methods with MATLAB for Engineers and Scientists

Author: Steven C. Chapra

Publisher: McGraw-Hill Science/Engineering/Math

Published: 2008

Total Pages: 618

ISBN-13:

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Still brief - but with the chapters that you wanted - Steven Chapra’s new second edition is written for engineering and science students who need to learn numerical problem solving. This text focuses on problem-solving applications rather than theory, using MATLAB throughout. Theory is introduced to inform key concepts which are framed in applications and demonstrated using MATLAB. The new second edition feature new chapters on Numerical Differentiation, Optimization, and Boundary-Value Problems (ODEs).

Engineering Electromagnetics
Engineering Electromagnetics

Author: Nathan Ida

Publisher: Springer

Published: 2015-03-20

Total Pages: 1062

ISBN-13: 3319078062

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This book provides students with a thorough theoretical understanding of electromagnetic field equations and it also treats a large number of applications. The text is a comprehensive two-semester textbook. The work treats most topics in two steps – a short, introductory chapter followed by a second chapter with in-depth extensive treatment; between 10 to 30 applications per topic; examples and exercises throughout the book; experiments, problems and summaries. The new edition includes: modifications to about 30-40% of the end of chapter problems; a new introduction to electromagnetics based on behavior of charges; a new section on units; MATLAB tools for solution of problems and demonstration of subjects; most chapters include a summary. The book is an undergraduate textbook at the Junior level, intended for required classes in electromagnetics. It is written in simple terms with all details of derivations included and all steps in solutions listed. It requires little beyond basic calculus and can be used for self-study. The wealth of examples and alternative explanations makes it very approachable by students. More than 400 examples and exercises, exercising every topic in the book Includes 600 end-of-chapter problems, many of them applications or simplified applications Discusses the finite element, finite difference and method of moments in a dedicated chapter

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

Author: Nikola? Iosifovich Ronto

Publisher: World Scientific

Published: 2000

Total Pages: 470

ISBN-13: 9789810236762

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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.

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

Published: 2024-11-01

Total Pages: 215

ISBN-13: 1040287425

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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.

First Course In Integral Equations, A (Second Edition)
First Course In Integral Equations, A (Second Edition)

Author: Abdul-majid Wazwaz

Publisher: World Scientific Publishing Company

Published: 2015-05-04

Total Pages: 327

ISBN-13: 9814675148

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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.

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

Author: Gehan Anthonys

Publisher: Springer Nature

Published: 2022-06-01

Total Pages: 102

ISBN-13: 3031020197

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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.

Innovative Computing Vol 1 - Emerging Topics in Artificial Intelligence
Innovative Computing Vol 1 - Emerging Topics in Artificial Intelligence

Author: Jason C. Hung

Publisher: Springer Nature

Published: 2023-06-02

Total Pages: 1042

ISBN-13: 9819920922

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This book comprises select peer-reviewed proceedings of the 6th International Conference on Innovative Computing (IC 2023). The contents focus on communication networks, business intelligence and knowledge management, web intelligence, and fields related to the development of information technology. The chapters include contributions on various topics such as databases and data mining, networking and communications, web and Internet of Things, embedded systems, soft computing, social network analysis, security and privacy, optical communication, and ubiquitous/pervasive computing. This volume will serve as a comprehensive overview of the latest advances in information technology for those working as researchers in both academia and industry.