Advanced Numerical And Semi Analytical Methods For Differential Equations

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Advanced Numerical and Semi-Analytical Methods for Differential Equations

Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Advanced Numerical and Semi Analytical Methods for Differential Equations Book PDF

Author : Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Publisher : John Wiley & Sons
Page : 256 pages
File Size : 42,6 Mb
Release : 2019-03-20
Category : Mathematics
ISBN : 9781119423447

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Advanced Numerical and Semi-Analytical Methods for Differential Equations by Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao Pdf

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.

Advanced Numerical and Semi-Analytical Methods for Differential Equations

Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Advanced Numerical and Semi Analytical Methods for Differential Equations Book PDF

Author : Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao
Publisher : John Wiley & Sons
Page : 256 pages
File Size : 55,8 Mb
Release : 2019-04-16
Category : Mathematics
ISBN : 9781119423423

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Advanced Numerical and Semi-Analytical Methods for Differential Equations by Snehashish Chakraverty,Nisha Mahato,Perumandla Karunakar,Tharasi Dilleswar Rao Pdf

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.

Numerical Analysis of Partial Differential Equations

S. H, Lui
Numerical Analysis of Partial Differential Equations Book PDF

Author : S. H, Lui
Publisher : John Wiley & Sons
Page : 506 pages
File Size : 51,5 Mb
Release : 2012-01-10
Category : Mathematics
ISBN : 9781118111116

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Numerical Analysis of Partial Differential Equations by S. H, Lui Pdf

A balanced guide to the essential techniques for solving elliptic partial differential equations Numerical Analysis of Partial Differential Equations provides a comprehensive, self-contained treatment of the quantitative methods used to solve elliptic partial differential equations (PDEs), with a focus on the efficiency as well as the error of the presented methods. The author utilizes coverage of theoretical PDEs, along with the nu merical solution of linear systems and various examples and exercises, to supply readers with an introduction to the essential concepts in the numerical analysis of PDEs. The book presents the three main discretization methods of elliptic PDEs: finite difference, finite elements, and spectral methods. Each topic has its own devoted chapters and is discussed alongside additional key topics, including: The mathematical theory of elliptic PDEs Numerical linear algebra Time-dependent PDEs Multigrid and domain decomposition PDEs posed on infinite domains The book concludes with a discussion of the methods for nonlinear problems, such as Newton's method, and addresses the importance of hands-on work to facilitate learning. Each chapter concludes with a set of exercises, including theoretical and programming problems, that allows readers to test their understanding of the presented theories and techniques. In addition, the book discusses important nonlinear problems in many fields of science and engineering, providing information as to how they can serve as computing projects across various disciplines. Requiring only a preliminary understanding of analysis, Numerical Analysis of Partial Differential Equations is suitable for courses on numerical PDEs at the upper-undergraduate and graduate levels. The book is also appropriate for students majoring in the mathematical sciences and engineering.

Advanced Numerical Methods with Matlab 2

Bouchaib Radi,Abdelkhalak El Hami
Advanced Numerical Methods with Matlab 2 Book PDF

Author : Bouchaib Radi,Abdelkhalak El Hami
Publisher : John Wiley & Sons
Page : 218 pages
File Size : 49,5 Mb
Release : 2018-05-24
Category : Mathematics
ISBN : 9781119527428

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Advanced Numerical Methods with Matlab 2 by Bouchaib Radi,Abdelkhalak El Hami Pdf

The purpose of this book is to introduce and study numerical methods basic and advanced ones for scientific computing. This last refers to the implementation of appropriate approaches to the treatment of a scientific problem arising from physics (meteorology, pollution, etc.) or of engineering (mechanics of structures, mechanics of fluids, treatment signal, etc.). Each chapter of this book recalls the essence of the different methods resolution and presents several applications in the field of engineering as well as programs developed under Matlab software.

Numerical Methods for Ordinary Differential Equations

J. C. Butcher
Numerical Methods for Ordinary Differential Equations Book PDF

Author : J. C. Butcher
Publisher : John Wiley & Sons
Page : 486 pages
File Size : 43,9 Mb
Release : 2008-04-15
Category : Mathematics
ISBN : 0470753757

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Numerical Methods for Ordinary Differential Equations by J. C. Butcher Pdf

In recent years the study of numerical methods for solving ordinary differential equations has seen many new developments. This second edition of the author's pioneering text is fully revised and updated to acknowledge many of these developments. It includes a complete treatment of linear multistep methods whilst maintaining its unique and comprehensive emphasis on Runge-Kutta methods and general linear methods. Although the specialist topics are taken to an advanced level, the entry point to the volume as a whole is not especially demanding. Early chapters provide a wide-ranging introduction to differential equations and difference equations together with a survey of numerical differential equation methods, based on the fundamental Euler method with more sophisticated methods presented as generalizations of Euler. Features of the book include Introductory work on differential and difference equations. A comprehensive introduction to the theory and practice of solving ordinary differential equations numerically. A detailed analysis of Runge-Kutta methods and of linear multistep methods. A complete study of general linear methods from both theoretical and practical points of view. The latest results on practical general linear methods and their implementation. A balance between informal discussion and rigorous mathematical style. Examples and exercises integrated into each chapter enhancing the suitability of the book as a course text or a self-study treatise. Written in a lucid style by one of the worlds leading authorities on numerical methods for ordinary differential equations and drawing upon his vast experience, this new edition provides an accessible and self-contained introduction, ideal for researchers and students following courses on numerical methods, engineering and other sciences.

Ordinary Differential Equations

Michael D. Greenberg
Ordinary Differential Equations Book PDF

Author : Michael D. Greenberg
Publisher : John Wiley & Sons
Page : 565 pages
File Size : 53,8 Mb
Release : 2014-05-29
Category : Mathematics
ISBN : 9781118243404

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Ordinary Differential Equations by Michael D. Greenberg Pdf

Features a balance between theory, proofs, and examples and provides applications across diverse fields of study Ordinary Differential Equations presents a thorough discussion of first-order differential equations and progresses to equations of higher order. The book transitions smoothly from first-order to higher-order equations, allowing readers to develop a complete understanding of the related theory. Featuring diverse and interesting applications from engineering, bioengineering, ecology, and biology, the book anticipates potential difficulties in understanding the various solution steps and provides all the necessary details. Topical coverage includes: First-Order Differential Equations Higher-Order Linear Equations Applications of Higher-Order Linear Equations Systems of Linear Differential Equations Laplace Transform Series Solutions Systems of Nonlinear Differential Equations In addition to plentiful exercises and examples throughout, each chapter concludes with a summary that outlines key concepts and techniques. The book's design allows readers to interact with the content, while hints, cautions, and emphasis are uniquely featured in the margins to further help and engage readers. Written in an accessible style that includes all needed details and steps, Ordinary Differential Equations is an excellent book for courses on the topic at the upper-undergraduate level. The book also serves as a valuable resource for professionals in the fields of engineering, physics, and mathematics who utilize differential equations in their everyday work. An Instructors Manual is available upon request. Email [email protected] for information. There is also a Solutions Manual available. The ISBN is 9781118398999.

Computational Fractional Dynamical Systems

Snehashish Chakraverty,Rajarama M. Jena,Subrat K. Jena
Computational Fractional Dynamical Systems Book PDF

Author : Snehashish Chakraverty,Rajarama M. Jena,Subrat K. Jena
Publisher : John Wiley & Sons
Page : 276 pages
File Size : 52,5 Mb
Release : 2022-11-15
Category : Mathematics
ISBN : 9781119696957

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Computational Fractional Dynamical Systems by Snehashish Chakraverty,Rajarama M. Jena,Subrat K. Jena Pdf

A rigorous presentation of different expansion and semi-analytical methods for fractional differential equations Fractional differential equations, differential and integral operators with non-integral powers, are used in various science and engineering applications. Over the past several decades, the popularity of the fractional derivative has increased significantly in diverse areas such as electromagnetics, financial mathematics, image processing, and materials science. Obtaining analytical and numerical solutions of nonlinear partial differential equations of fractional order can be challenging and involve the development and use of different methods of solution. Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications presents a variety of computationally efficient semi-analytical and expansion methods to solve different types of fractional models. Rather than focusing on a single computational method, this comprehensive volume brings together more than 25 methods for solving an array of fractional-order models. The authors employ a rigorous and systematic approach for addressing various physical problems in science and engineering. Covers various aspects of efficient methods regarding fractional-order systems Presents different numerical methods with detailed steps to handle basic and advanced equations in science and engineering Provides a systematic approach for handling fractional-order models arising in science and engineering Incorporates a wide range of methods with corresponding results and validation Computational Fractional Dynamical Systems: Fractional Differential Equations and Applications is an invaluable resource for advanced undergraduate students, graduate students, postdoctoral researchers, university faculty, and other researchers and practitioners working with fractional and integer order differential equations.

Advanced Numerical Methods for Differential Equations

Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar
Advanced Numerical Methods for Differential Equations Book PDF

Author : Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar
Publisher : Unknown
Page : 232 pages
File Size : 42,7 Mb
Release : 2021
Category : Differential equations
ISBN : 0367473119

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Advanced Numerical Methods for Differential Equations by Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar Pdf

Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

Numerical Methods for Ordinary Differential Equations

J. C. Butcher
Numerical Methods for Ordinary Differential Equations Book PDF

Author : J. C. Butcher
Publisher : John Wiley & Sons
Page : 442 pages
File Size : 45,7 Mb
Release : 2004-08-20
Category : Mathematics
ISBN : 9780470868263

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Numerical Methods for Ordinary Differential Equations by J. C. Butcher Pdf

This new book updates the exceptionally popular Numerical Analysis of Ordinary Differential Equations. "This book is...an indispensible reference for any researcher."-American Mathematical Society on the First Edition. Features: * New exercises included in each chapter. * Author is widely regarded as the world expert on Runge-Kutta methods * Didactic aspects of the book have been enhanced by interspersing the text with exercises. * Updated Bibliography.

Partial Differential Equations

Mark S. Gockenbach
Partial Differential Equations Book PDF

Author : Mark S. Gockenbach
Publisher : SIAM
Page : 665 pages
File Size : 55,6 Mb
Release : 2010-12-02
Category : Mathematics
ISBN : 9780898719352

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Partial Differential Equations by Mark S. Gockenbach Pdf

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

A First Course in Ordinary Differential Equations

Martin Hermann,Masoud Saravi
A First Course in Ordinary Differential Equations Book PDF

Author : Martin Hermann,Masoud Saravi
Publisher : Springer
Page : 0 pages
File Size : 44,9 Mb
Release : 2016-09-03
Category : Mathematics
ISBN : 8132235274

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A First Course in Ordinary Differential Equations by Martin Hermann,Masoud Saravi Pdf

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 ODEs—with a special focus on the Laplace transform, operator techniques and power series solutions. In the numerical part, theoretical and practical aspects of Runge-Kutta methods for solving initial-value problems and shooting methods for linear two-point boundary-value problems are considered. The book is intended as a primary text for courses on the theory of ODEs and numerical treatment of ODEs for advanced undergraduate and early graduate students. It is assumed that the reader has a basic grasp of elementary calculus, in particular methods of integration, and of numerical analysis. Physicists, chemists, biologists, computer scientists and engineers whose work involves solving ODEs will also find the book useful as a reference work and tool for independent study. The book has been prepared within the framework of a German–Iranian research project on mathematical methods for ODEs, which was started in early 2012.

Advanced Numerical Methods for Differential Equations

Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar
Advanced Numerical Methods for Differential Equations Book PDF

Author : Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar
Publisher : CRC Press
Page : 336 pages
File Size : 54,9 Mb
Release : 2021-07-29
Category : Mathematics
ISBN : 9781000381085

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Advanced Numerical Methods for Differential Equations by Harendra Singh,Jagdev Singh,Sunil Dutt Purohit,Devendra Kumar Pdf

Mathematical models are used to convert real-life problems using mathematical concepts and language. These models are governed by differential equations whose solutions make it easy to understand real-life problems and can be applied to engineering and science disciplines. This book presents numerical methods for solving various mathematical models. This book offers real-life applications, includes research problems on numerical treatment, and shows how to develop the numerical methods for solving problems. The book also covers theory and applications in engineering and science. Engineers, mathematicians, scientists, and researchers working on real-life mathematical problems will find this book useful.

Numerical Solution of Ordinary Differential Equations

Kendall Atkinson,Weimin Han,David E. Stewart
Numerical Solution of Ordinary Differential Equations Book PDF

Author : Kendall Atkinson,Weimin Han,David E. Stewart
Publisher : John Wiley & Sons
Page : 272 pages
File Size : 40,5 Mb
Release : 2011-10-24
Category : Mathematics
ISBN : 9781118164525

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Numerical Solution of Ordinary Differential Equations by Kendall Atkinson,Weimin Han,David E. Stewart Pdf

A concise introduction to numerical methodsand the mathematicalframework neededto understand their performance Numerical Solution of Ordinary Differential Equationspresents a complete and easy-to-follow introduction to classicaltopics in the numerical solution of ordinary differentialequations. The book's approach not only explains the presentedmathematics, but also helps readers understand how these numericalmethods are used to solve real-world problems. Unifying perspectives are provided throughout the text, bringingtogether and categorizing different types of problems in order tohelp readers comprehend the applications of ordinary differentialequations. In addition, the authors' collective academic experienceensures a coherent and accessible discussion of key topics,including: Euler's method Taylor and Runge-Kutta methods General error analysis for multi-step methods Stiff differential equations Differential algebraic equations Two-point boundary value problems Volterra integral equations Each chapter features problem sets that enable readers to testand build their knowledge of the presented methods, and a relatedWeb site features MATLAB® programs that facilitate theexploration of numerical methods in greater depth. Detailedreferences outline additional literature on both analytical andnumerical aspects of ordinary differential equations for furtherexploration of individual topics. Numerical Solution of Ordinary Differential Equations isan excellent textbook for courses on the numerical solution ofdifferential equations at the upper-undergraduate and beginninggraduate levels. It also serves as a valuable reference forresearchers in the fields of mathematics and engineering.

Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations

Geeta Arora,Mangey Ram
Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations Book PDF

Author : Geeta Arora,Mangey Ram
Publisher : CRC Press
Page : 177 pages
File Size : 46,9 Mb
Release : 2024-01-23
Category : Mathematics
ISBN : 9781003811022

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Advance Numerical Techniques to Solve Linear and Nonlinear Differential Equations by Geeta Arora,Mangey Ram Pdf

Real-world issues can be translated into the language and concepts of mathematics with the use of mathematical models. Models guided by differential equations with intuitive solutions can be used throughout engineering and the sciences. Almost any changing system may be described by a set of differential equations. They may be found just about anywhere you look in fields including physics, engineering, economics, sociology, biology, business, healthcare, etc. The nature of these equations has been investigated by several mathematicians over the course of hundreds of years and, consequently, numerous effective methods for solving them have been created. It is often impractical to find a purely analytical solution to a system described by a differential equation because either the system itself is too complex or the system being described is too vast. Numerical approaches and computer simulations are especially helpful in such systems. The content provided in this book involves real-world examples, explores research challenges in numerical treatment, and demonstrates how to create new numerical methods for resolving problems. Theories and practical applications in the sciences and engineering are also discussed. Students of engineering and applied mathematics, as well as researchers and engineers who use computers to solve problems numerically or oversee those who do, will find this book focusing on advance numerical techniques to solve linear and nonlinear differential equations useful.

Numerical Methods for Special Functions

Amparo Gil,Javier Segura,Nico M. Temme
Numerical Methods for Special Functions Book PDF

Author : Amparo Gil,Javier Segura,Nico M. Temme
Publisher : SIAM
Page : 431 pages
File Size : 41,5 Mb
Release : 2007-01-01
Category : Mathematics
ISBN : 0898717825

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Numerical Methods for Special Functions by Amparo Gil,Javier Segura,Nico M. Temme Pdf

Special functions arise in many problems of pure and applied mathematics, mathematical statistics, physics, and engineering. This book provides an up-to-date overview of numerical methods for computing special functions and discusses when to use these methods depending on the function and the range of parameters. Not only are standard and simple parameter domains considered, but methods valid for large and complex parameters are described as well. The first part of the book (basic methods) covers convergent and divergent series, Chebyshev expansions, numerical quadrature, and recurrence relations. Its focus is on the computation of special functions; however, it is suitable for general numerical courses. Pseudoalgorithms are given to help students write their own algorithms. In addition to these basic tools, the authors discuss other useful and efficient methods, such as methods for computing zeros of special functions, uniform asymptotic expansions, Padé approximations, and sequence transformations. The book also provides specific algorithms for computing several special functions (like Airy functions and parabolic cylinder functions, among others).