Numerical Solutions Of Nonlinear Differential Equations

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Numerical Methods for Nonlinear Partial Differential Equations

Author : Sören Bartels
Publisher : Springer
ISBN 13 : 3319137972
Total Pages : 394 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Numerical Methods for Nonlinear Partial Differential Equations by : Sören Bartels

Download or read book Numerical Methods for Nonlinear Partial Differential Equations written by Sören Bartels and published by Springer. This book was released on 2015-01-19 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

Numerical Solutions of Nonlinear Differential Equations

Author : Donald Greenspan
Publisher :
ISBN 13 :
Total Pages : 368 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Numerical Solutions of Nonlinear Differential Equations by : Donald Greenspan

Download or read book Numerical Solutions of Nonlinear Differential Equations written by Donald Greenspan and published by . This book was released on 1966 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Ordinary Differential Equations

Author : R. Grimshaw
Publisher : Routledge
ISBN 13 : 135142808X
Total Pages : 342 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Nonlinear Ordinary Differential Equations by : R. Grimshaw

Download or read book Nonlinear Ordinary Differential Equations written by R. Grimshaw and published by Routledge. This book was released on 2017-10-19 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.

Numerical Solution of Ordinary Differential Equations

Author : L.F. Shampine
Publisher : Routledge
ISBN 13 : 1351427555
Total Pages : 632 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Numerical Solution of Ordinary Differential Equations by : L.F. Shampine

Download or read book Numerical Solution of Ordinary Differential Equations written by L.F. Shampine and published by Routledge. This book was released on 2018-10-24 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations. The first three chapters are general in nature, and chapters 4 through 8 derive the basic numerical methods, prove their convergence, study their stability and consider how to implement them effectively. The book focuses on the most important methods in practice and develops them fully, uses examples throughout, and emphasizes practical problem-solving methods.

Numerical Solutions of Boundary Value Problems of Non-Linear Differential Equations

Author : Sujaul Chowdhury
Publisher : Chapman & Hall/CRC
ISBN 13 : 9781003204916
Total Pages : 102 pages
Book Rating : 4.2/5 (49 download)

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Book Synopsis Numerical Solutions of Boundary Value Problems of Non-Linear Differential Equations by : Sujaul Chowdhury

Download or read book Numerical Solutions of Boundary Value Problems of Non-Linear Differential Equations written by Sujaul Chowdhury and published by Chapman & Hall/CRC. This book was released on 2021-10-25 with total page 102 pages. Available in PDF, EPUB and Kindle. Book 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 of Non-linear Differential Equations

Author : Sujaul Chowdhury
Publisher : CRC Press
ISBN 13 : 1000486141
Total Pages : 77 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Numerical Solutions of Boundary Value Problems of Non-linear Differential Equations by : Sujaul Chowdhury

Download or read book Numerical Solutions of Boundary Value Problems of Non-linear Differential Equations written by Sujaul Chowdhury and published by CRC Press. This book was released on 2021-10-25 with total page 77 pages. Available in PDF, EPUB and Kindle. Book 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.

Recent Developments in the Solution of Nonlinear Differential Equations

Author : Bruno Carpentieri
Publisher : BoD – Books on Demand
ISBN 13 : 1839686561
Total Pages : 374 pages
Book Rating : 4.8/5 (396 download)

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Book Synopsis Recent Developments in the Solution of Nonlinear Differential Equations by : Bruno Carpentieri

Download or read book Recent Developments in the Solution of Nonlinear Differential Equations written by Bruno Carpentieri and published by BoD – Books on Demand. This book was released on 2021-09-08 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear differential equations are ubiquitous in computational science and engineering modeling, fluid dynamics, finance, and quantum mechanics, among other areas. Nowadays, solving challenging problems in an industrial setting requires a continuous interplay between the theory of such systems and the development and use of sophisticated computational methods that can guide and support the theoretical findings via practical computer simulations. Owing to the impressive development in computer technology and the introduction of fast numerical methods with reduced algorithmic and memory complexity, rigorous solutions in many applications have become possible. This book collects research papers from leading world experts in the field, highlighting ongoing trends, progress, and open problems in this critically important area of mathematics.

Numerical Solutions of Nonlinear Differential Equations

Author : Donald Greenspan
Publisher :
ISBN 13 :
Total Pages : 347 pages
Book Rating : 4.:/5 (225 download)

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Book Synopsis Numerical Solutions of Nonlinear Differential Equations by : Donald Greenspan

Download or read book Numerical Solutions of Nonlinear Differential Equations written by Donald Greenspan and published by . This book was released on 1966 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Solution of Nonlinear Boundary Value Problems with Applications

Author : Milan Kubicek
Publisher : Courier Corporation
ISBN 13 : 0486463001
Total Pages : 338 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Numerical Solution of Nonlinear Boundary Value Problems with Applications by : Milan Kubicek

Download or read book Numerical Solution of Nonlinear Boundary Value Problems with Applications written by Milan Kubicek and published by Courier Corporation. This book was released on 2008-01-01 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey of the development, analysis, and application of numerical techniques in solving nonlinear boundary value problems, this text presents numerical analysis as a working tool for physicists and engineers. Starting with a survey of accomplishments in the field, it explores initial and boundary value problems for ordinary differential equations, linear boundary value problems, and the numerical realization of parametric studies in nonlinear boundary value problems. The authors--Milan Kubicek, Professor at the Prague Institute of Chemical Technology, and Vladimir Hlavacek, Professor at the University of Buffalo--emphasize the description and straightforward application of numerical techniques rather than underlying theory. This approach reflects their extensive experience with the application of diverse numerical algorithms.

Nonlinear Ordinary Differential Equations

Author : Martin Hermann
Publisher : Springer
ISBN 13 : 813222812X
Total Pages : 320 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Nonlinear Ordinary Differential Equations by : Martin Hermann

Download or read book Nonlinear Ordinary Differential Equations written by Martin Hermann and published by Springer. This book was released on 2016-05-09 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 solving nonlinear ODEs using numerical methods, as in practice high-dimensional systems of nonlinear ODEs that cannot be solved by analytical approximate methods are common. Moreover, it studies analytical and numerical techniques for the treatment of parameter-depending ODEs. The book explains various methods for solving nonlinear-oscillator and structural-system problems, including the energy balance method, harmonic balance method, amplitude frequency formulation, variational iteration method, homotopy perturbation method, iteration perturbation method, homotopy analysis method, simple and multiple shooting method, and the nonlinear stabilized march method. This book comprehensively investigates various new analytical and numerical approximation techniques that are used in solving nonlinear-oscillator and structural-system problems. Students often rely on the finite element method to such an extent that on graduation they have little or no knowledge of alternative methods of solving problems. To rectify this, the book introduces several new approximation techniques.

Solving Nonlinear Partial Differential Equations with Maple and Mathematica

Author : Inna Shingareva
Publisher : Springer Science & Business Media
ISBN 13 : 370910517X
Total Pages : 372 pages
Book Rating : 4.7/5 (91 download)

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Book Synopsis Solving Nonlinear Partial Differential Equations with Maple and Mathematica by : Inna Shingareva

Download or read book Solving Nonlinear Partial Differential Equations with Maple and Mathematica written by Inna Shingareva and published by Springer Science & Business Media. This book was released on 2011-07-24 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emphasis of the book is given in how to construct different types of solutions (exact, approximate analytical, numerical, graphical) of numerous nonlinear PDEs correctly, easily, and quickly. The reader can learn a wide variety of techniques and solve numerous nonlinear PDEs included and many other differential equations, simplifying and transforming the equations and solutions, arbitrary functions and parameters, presented in the book). Numerous comparisons and relationships between various types of solutions, different methods and approaches are provided, the results obtained in Maple and Mathematica, facilitates a deeper understanding of the subject. Among a big number of CAS, we choose the two systems, Maple and Mathematica, that are used worldwide by students, research mathematicians, scientists, and engineers. As in the our previous books, we propose the idea to use in parallel both systems, Maple and Mathematica, since in many research problems frequently it is required to compare independent results obtained by using different computer algebra systems, Maple and/or Mathematica, at all stages of the solution process. One of the main points (related to CAS) is based on the implementation of a whole solution method (e.g. starting from an analytical derivation of exact governing equations, constructing discretizations and analytical formulas of a numerical method, performing numerical procedure, obtaining various visualizations, and comparing the numerical solution obtained with other types of solutions considered in the book, e.g. with asymptotic solution).

Introduction to Numerical Methods in Differential Equations

Author : Mark H. Holmes
Publisher : Springer Science & Business Media
ISBN 13 : 0387681213
Total Pages : 248 pages
Book Rating : 4.3/5 (876 download)

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Book Synopsis Introduction to Numerical Methods in Differential Equations by : Mark H. Holmes

Download or read book Introduction to Numerical Methods in Differential Equations written by Mark H. Holmes and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.

PETSc for Partial Differential Equations: Numerical Solutions in C and Python

Author : Ed Bueler
Publisher : SIAM
ISBN 13 : 1611976316
Total Pages : 407 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis PETSc for Partial Differential Equations: Numerical Solutions in C and Python by : Ed Bueler

Download or read book PETSc for Partial Differential Equations: Numerical Solutions in C and Python written by Ed Bueler and published by SIAM. This book was released on 2020-10-22 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

Numerical Solution of Boundary Value Problems for Ordinary Differential Equations

Author : Uri M. Ascher
Publisher : SIAM
ISBN 13 : 9781611971231
Total Pages : 620 pages
Book Rating : 4.9/5 (712 download)

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Book Synopsis Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by : Uri M. Ascher

Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1994-12-01 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.

Numerical Solution of Ordinary Differential Equations

Author : Kendall Atkinson
Publisher : John Wiley & Sons
ISBN 13 : 1118164520
Total Pages : 272 pages
Book Rating : 4.1/5 (181 download)

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Book Synopsis Numerical Solution of Ordinary Differential Equations by : Kendall Atkinson

Download or read book Numerical Solution of Ordinary Differential Equations written by Kendall Atkinson and published by John Wiley & Sons. This book was released on 2011-10-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Solution of Differential Equations

Author : Zhilin Li
Publisher : Cambridge University Press
ISBN 13 : 1107163226
Total Pages : 305 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Numerical Solution of Differential Equations by : Zhilin Li

Download or read book Numerical Solution of Differential Equations written by Zhilin Li and published by Cambridge University Press. This book was released on 2017-11-30 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical and concise guide to finite difference and finite element methods. Well-tested MATLAB® codes are available online.

Numerical Methods for Nonlinear Engineering Models

Author : John R. Hauser
Publisher : Springer Science & Business Media
ISBN 13 : 1402099207
Total Pages : 1013 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Numerical Methods for Nonlinear Engineering Models by : John R. Hauser

Download or read book Numerical Methods for Nonlinear Engineering Models written by John R. Hauser and published by Springer Science & Business Media. This book was released on 2009-03-24 with total page 1013 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.