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Computer Methods In Solution Of Differential Equations
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Book Synopsis Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations by : Uri M. Ascher
Download or read book Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations written by Uri M. Ascher and published by SIAM. This book was released on 1998-01-01 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for those people who want to gain a practical knowledge of modern techniques, this book contains all the material necessary for a course on the numerical solution of differential equations. Written by two of the field's leading authorities, it provides a unified presentation of initial value and boundary value problems in ODEs as well as differential-algebraic equations. The approach is aimed at a thorough understanding of the issues and methods for practical computation while avoiding an extensive theorem-proof type of exposition. It also addresses reasons why existing software succeeds or fails. This book is a practical and mathematically well-informed introduction that emphasizes basic methods and theory, issues in the use and development of mathematical software, and examples from scientific engineering applications. Topics requiring an extensive amount of mathematical development, such as symplectic methods for Hamiltonian systems, are introduced, motivated, and included in the exercises, but a complete and rigorous mathematical presentation is referenced rather than included.
Book Synopsis Computer Methods in Solution of Differential Equations by : Jørgen Kjær
Download or read book Computer Methods in Solution of Differential Equations written by Jørgen Kjær and published by . This book was released on 1971 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Differential Equations by : J.R. Dormand
Download or read book Numerical Methods for Differential Equations written by J.R. Dormand and published by CRC Press. This book was released on 2018-05-04 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran 90. These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations. Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations.
Book Synopsis Computational Differential Equations by : Kenneth Eriksson
Download or read book Computational Differential Equations written by Kenneth Eriksson and published by Cambridge University Press. This book was released on 1996-09-05 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook on computational mathematics is based on a fusion of mathematical analysis, numerical computation and applications.
Book Synopsis Numerical Methods for Differential Equations by : J.R. Dormand
Download or read book Numerical Methods for Differential Equations written by J.R. Dormand and published by CRC Press. This book was released on 2018-05-04 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: With emphasis on modern techniques, Numerical Methods for Differential Equations: A Computational Approach covers the development and application of methods for the numerical solution of ordinary differential equations. Some of the methods are extended to cover partial differential equations. All techniques covered in the text are on a program disk included with the book, and are written in Fortran 90. These programs are ideal for students, researchers, and practitioners because they allow for straightforward application of the numerical methods described in the text. The code is easily modified to solve new systems of equations. Numerical Methods for Differential Equations: A Computational Approach also contains a reliable and inexpensive global error code for those interested in global error estimation. This is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use. It is also an excellent reference and source of software for researchers and practitioners who need computer solutions to differential equations.
Book Synopsis Advances in Computer Methods for Partial Differential Equations-III by : Robert Vichnevetsky
Download or read book Advances in Computer Methods for Partial Differential Equations-III written by Robert Vichnevetsky and published by . This book was released on 1979 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: One Thursday Imogene wakes up with a pair of antlers growing out of her head and causes a sensation.
Book Synopsis Advances in Computer Methods for Partial Differential Equations by :
Download or read book Advances in Computer Methods for Partial Differential Equations written by and published by . This book was released on 1987 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific Computing and Differential Equations by : Gene H. Golub
Download or read book Scientific Computing and Differential Equations written by Gene H. Golub and published by Elsevier. This book was released on 2014-06-28 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific Computing and Differential Equations: An Introduction to Numerical Methods, is an excellent complement to Introduction to Numerical Methods by Ortega and Poole. The book emphasizes the importance of solving differential equations on a computer, which comprises a large part of what has come to be called scientific computing. It reviews modern scientific computing, outlines its applications, and places the subject in a larger context. This book is appropriate for upper undergraduate courses in mathematics, electrical engineering, and computer science; it is also well-suited to serve as a textbook for numerical differential equations courses at the graduate level. An introductory chapter gives an overview of scientific computing, indicating its important role in solving differential equations, and placing the subject in the larger environment Contains an introduction to numerical methods for both ordinary and partial differential equations Concentrates on ordinary differential equations, especially boundary-value problems Contains most of the main topics for a first course in numerical methods, and can serve as a text for this course Uses material for junior/senior level undergraduate courses in math and computer science plus material for numerical differential equations courses for engineering/science students at the graduate level
Book Synopsis Automated Solution of Differential Equations by the Finite Element Method by : Anders Logg
Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.
Book Synopsis Computing Methods by : I. S. Berezin
Download or read book Computing Methods written by I. S. Berezin and published by Elsevier. This book was released on 2014-05-16 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computing Methods, Volume 2 is a five-chapter text that presents the numerical methods of solving sets of several mathematical equations. This volume includes computation sets of linear algebraic equations, high degree equations and transcendental equations, numerical methods of finding eigenvalues, and approximate methods of solving ordinary differential equations, partial differential equations and integral equations. The book is intended as a text-book for students in mechanical mathematical and physics-mathematical faculties specializing in computer mathematics and persons interested in the theory and practice of numerical methods.
Book Synopsis Computer Solution of Ordinary Differential Equations by : Lawrence F. Shampine
Download or read book Computer Solution of Ordinary Differential Equations written by Lawrence F. Shampine and published by W.H. Freeman. This book was released on 1975 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Numerical Methods for Evolutionary Differential Equations by : Uri M. Ascher
Download or read book Numerical Methods for Evolutionary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 2008-09-04 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.
Book Synopsis A Practical Guide to Computer Methods for Engineers by : Terry E. Shoup
Download or read book A Practical Guide to Computer Methods for Engineers written by Terry E. Shoup and published by Prentice Hall. This book was released on 1979 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances in Computer Methods for Partial Differential Equations by : Robert Vichnevetsky
Download or read book Advances in Computer Methods for Partial Differential Equations written by Robert Vichnevetsky and published by . This book was released on 1975 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computer Solution of Large Linear Systems by : Gerard Meurant
Download or read book Computer Solution of Large Linear Systems written by Gerard Meurant and published by Elsevier. This book was released on 1999-06-16 with total page 777 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with numerical methods for solving large sparse linear systems of equations, particularly those arising from the discretization of partial differential equations. It covers both direct and iterative methods. Direct methods which are considered are variants of Gaussian elimination and fast solvers for separable partial differential equations in rectangular domains. The book reviews the classical iterative methods like Jacobi, Gauss-Seidel and alternating directions algorithms. A particular emphasis is put on the conjugate gradient as well as conjugate gradient -like methods for non symmetric problems. Most efficient preconditioners used to speed up convergence are studied. A chapter is devoted to the multigrid method and the book ends with domain decomposition algorithms that are well suited for solving linear systems on parallel computers.
Book Synopsis Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations by : Mitsuhiro T. Nakao
Download or read book Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations written by Mitsuhiro T. Nakao and published by Springer Nature. This book was released on 2019-11-11 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.
