Analytical Methods In Differential Equations

DOWNLOAD

Download Analytical Methods In Differential Equations PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Analytical Methods In Differential Equations book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Analytic Methods For Partial Differential Equations

DOWNLOAD
Author : G. Evans
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Analytic Methods For Partial Differential Equations written by G. Evans and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The subject of partial differential equations holds an exciting and special position in mathematics. Partial differential equations were not consciously created as a subject but emerged in the 18th century as ordinary differential equations failed to describe the physical principles being studied. The subject was originally developed by the major names of mathematics, in particular, Leonard Euler and Joseph-Louis Lagrange who studied waves on strings; Daniel Bernoulli and Euler who considered potential theory, with later developments by Adrien-Marie Legendre and Pierre-Simon Laplace; and Joseph Fourier's famous work on series expansions for the heat equation. Many of the greatest advances in modern science have been based on discovering the underlying partial differential equation for the process in question. J ames Clerk Maxwell, for example, put electricity and magnetism into a unified theory by estab lishing Maxwell's equations for electromagnetic theory, which gave solutions for problems in radio wave propagation, the diffraction of light and X-ray developments. Schrodinger's equation for quantum mechankal processes at the atomic level leads to experimentally verifiable results which have changed the face of atomic physics and chemistry in the 20th century. In fluid mechanics, the Navier-Stokes' equations form a basis for huge number-crunching activities associated with such widely disparate topics as weather forcasting and the design of supersonic aircraft. Inevitably the study of partial differential equations is a large undertaking, and falls into several areas of mathematics.

Methods For Constructing Exact Solutions Of Partial Differential Equations

DOWNLOAD
Author : Sergey V. Meleshko
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-18

Methods For Constructing Exact Solutions Of Partial Differential Equations written by Sergey V. Meleshko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-18 with Technology & Engineering categories.

Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

Analysis Of Approximation Methods For Differential And Integral Equations

DOWNLOAD
Author : Hans-Jürgen Reinhardt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Analysis Of Approximation Methods For Differential And Integral Equations written by Hans-Jürgen Reinhardt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite difference methods and of projection methods for approximating their variational formulations.

Analytical Methods In Differential Equations

DOWNLOAD
Author : Sergey V. Meleshko
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2025-02-17

Analytical Methods In Differential Equations written by Sergey V. Meleshko and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-17 with Mathematics categories.

The book compiles papers presented at the International Conference 'Advances in Applications of Analytical Methods in Solving Differential Equations', held in honour of Academician Lev V. Ovsiannikov’s 105th birthday anniversary. This collection reflects his extensive contributions to the theory of differential equations, modelling, and the application of analytical methods. In addition to classical methods such as analytical integration of systems of equations and their applications in various fields of Science and Engineering, the book explores new areas of research. This includes the application of group analysis to novel mathematical models and nonlinear problems, particularly equations with nonlocal terms (symmetries of difference and differential equations, as well as fractional differential equations). One of the notable contributions in the book is the development of a Hamiltonian approach for delay differential equations, representing a novel area of research that has not been previously explored. The book is anticipated to appeal to a broad audience of experts in applied mathematics, fluid dynamics, and modelling, as well as to young scientists and graduate students interested in the analysis of nonlinear equations.

Methods Of Applied Mathematics For Engineers And Scientists

DOWNLOAD
Author : Tomas B. Co
language : en
Publisher: Cambridge University Press
Release Date : 2013-06-28

Methods Of Applied Mathematics For Engineers And Scientists written by Tomas B. Co and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-28 with Mathematics categories.

This engineering mathematics textbook is rich with examples, applications and exercises, and emphasises applying matrices.

Advanced Numerical And Semi Analytical Methods For Differential Equations

DOWNLOAD
Author : Snehashish Chakraverty
language : en
Publisher: John Wiley & Sons
Release Date : 2019-03-20

Advanced Numerical And Semi Analytical Methods For Differential Equations written by Snehashish Chakraverty and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-20 with Mathematics categories.

Examines numerical and semi-analytical methods for differential equations that can be used for solving practical ODEs and PDEs This student-friendly book deals with various approaches for solving differential equations numerically or semi-analytically depending on the type of equations and offers simple example problems to help readers along. Featuring both traditional and recent methods, Advanced Numerical and Semi Analytical Methods for Differential Equations begins with a review of basic numerical methods. It then looks at Laplace, Fourier, and weighted residual methods for solving differential equations. A new challenging method of Boundary Characteristics Orthogonal Polynomials (BCOPs) is introduced next. The book then discusses Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM), and Boundary Element Method (BEM). Following that, analytical/semi analytic methods like Akbari Ganji's Method (AGM) and Exp-function are used to solve nonlinear differential equations. Nonlinear differential equations using semi-analytical methods are also addressed, namely Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), and Homotopy Analysis Method (HAM). Other topics covered include: emerging areas of research related to the solution of differential equations based on differential quadrature and wavelet approach; combined and hybrid methods for solving differential equations; as well as an overview of fractal differential equations. Further, uncertainty in term of intervals and fuzzy numbers have also been included, along with the interval finite element method. This book: Discusses various methods for solving linear and nonlinear ODEs and PDEs Covers basic numerical techniques for solving differential equations along with various discretization methods Investigates nonlinear differential equations using semi-analytical methods Examines differential equations in an uncertain environment Includes a new scenario in which uncertainty (in term of intervals and fuzzy numbers) has been included in differential equations Contains solved example problems, as well as some unsolved problems for self-validation of the topics covered Advanced Numerical and Semi Analytical Methods for Differential Equations is an excellent text for graduate as well as post graduate students and researchers studying various methods for solving differential equations, numerically and semi-analytically.

Homotopy Analysis Method In Nonlinear Differential Equations

DOWNLOAD
Author : Shijun Liao
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-22

Homotopy Analysis Method In Nonlinear Differential Equations written by Shijun Liao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-22 with Mathematics categories.

"Homotopy Analysis Method in Nonlinear Differential Equations" presents the latest developments and applications of the analytic approximation method for highly nonlinear problems, namely the homotopy analysis method (HAM). Unlike perturbation methods, the HAM has nothing to do with small/large physical parameters. In addition, it provides great freedom to choose the equation-type of linear sub-problems and the base functions of a solution. Above all, it provides a convenient way to guarantee the convergence of a solution. This book consists of three parts. Part I provides its basic ideas and theoretical development. Part II presents the HAM-based Mathematica package BVPh 1.0 for nonlinear boundary-value problems and its applications. Part III shows the validity of the HAM for nonlinear PDEs, such as the American put option and resonance criterion of nonlinear travelling waves. New solutions to a number of nonlinear problems are presented, illustrating the originality of the HAM. Mathematica codes are freely available online to make it easy for readers to understand and use the HAM. This book is suitable for researchers and postgraduates in applied mathematics, physics, nonlinear mechanics, finance and engineering. Dr. Shijun Liao, a distinguished professor of Shanghai Jiao Tong University, is a pioneer of the HAM.

Partial Differential Equations

DOWNLOAD
Author : Mark S. Gockenbach
language : en
Publisher: SIAM
Release Date : 2010-12-02

Partial Differential Equations written by Mark S. Gockenbach and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-12-02 with Mathematics categories.

A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.

Introduction To Numerical Methods In Differential Equations

DOWNLOAD
Author : Mark H. Holmes
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-05

Introduction To Numerical Methods In Differential Equations written by Mark H. Holmes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-05 with Mathematics categories.

The title gives a reasonable ?rst-order approximation to what this book is about. To explain why, let’s start with the expression “di?erential equations.” These are essential in science and engineering, because the laws of nature t- ically result in equations relating spatial and temporal changes in one or more variables.Todevelopanunderstandingofwhatisinvolvedin?ndingsolutions, the book begins with problems involving derivatives for only one independent variable, and these give rise to ordinary di?erential equations. Speci?cally, the ?rst chapter considers initial value problems (time derivatives), and the second concentrates on boundary value problems (space derivatives). In the succeeding four chapters problems involving both time and space derivatives, partial di?erential equations, are investigated. This brings us to the next expression in the title: “numerical methods.” This is a book about how to transform differential equations into problems that can be solved using a computer.The fact is that computers are only able to solve discrete problems and generally do this using ?nite-precision arithmetic. What this means is that in deriving and then using a numerical algorithmthecorrectnessofthediscreteapproximationmustbeconsidered,as must the consequences of round-o? error in using ?oating-point arithmetic to calculatetheanswer.Oneoftheinterestingaspectsofthesubjectisthatwhat appears to be an obviously correct numerical method can result in complete failure. Consequently, although the book concentrates on the derivation and use of numerical methods, the theoretical underpinnings are also presented andusedinthedevelopment.

Decomposition Analysis Method In Linear And Nonlinear Differential Equations

DOWNLOAD
Author : Kansari Haldar
language : en
Publisher: CRC Press
Release Date : 2015-10-22

Decomposition Analysis Method In Linear And Nonlinear Differential Equations written by Kansari Haldar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-22 with Mathematics categories.

A Powerful Methodology for Solving All Types of Differential EquationsDecomposition Analysis Method in Linear and Non-Linear Differential Equations explains how the Adomian decomposition method can solve differential equations for the series solutions of fundamental problems in physics, astrophysics, chemistry, biology, medicine, and other scientif