Nonlinear Implicit One Step Schemes For Solving Initial Value Problems For Ordinary Differential Equations With Steep Gradients

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Nonlinear Implicit One-Step Schemes for Solving Initial Value Problems for Ordinary Differential Equations with Steep Gradients

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Author : Jiachang Sun
Publisher :
ISBN 13 :
Total Pages : 33 pages
Book Rating : 4.:/5 (227 download)

Book Synopsis Nonlinear Implicit One-Step Schemes for Solving Initial Value Problems for Ordinary Differential Equations with Steep Gradients by : Jiachang Sun

Download or read book Nonlinear Implicit One-Step Schemes for Solving Initial Value Problems for Ordinary Differential Equations with Steep Gradients written by Jiachang Sun and published by . This book was released on 1982 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt: A general theory for nonlinear implicit one-step schemes for solving initial value problems for ordinary differential equations is presented in this paper. The general expansion of 'symmetric' implicit one-step schemes having second-order is derived and stability and convergence are studied. As examples, some geometric schemes are given. Based on previous work of the first author on a Generalization of Means, a fourth-order nonlinear implicit one-step scheme (GMS) is presented for solving equations with steep gradients. Also, a hybrid method based on the GMS and a fourth-order linear scheme is discussed. Some numerical results are given. (Author).

Scientific and Technical Aerospace Reports

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Author :
Publisher :
ISBN 13 :
Total Pages : 756 pages
Book Rating : 4.:/5 (31 download)

Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1983 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Numerical Methods for Initial Value Problems in Ordinary Differential Equations

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Author : Simeon Ola Fatunla
Publisher : Academic Press
ISBN 13 : 1483269264
Total Pages : 308 pages
Book Rating : 4.4/5 (832 download)

Book Synopsis Numerical Methods for Initial Value Problems in Ordinary Differential Equations by : Simeon Ola Fatunla

Download or read book Numerical Methods for Initial Value Problems in Ordinary Differential Equations written by Simeon Ola Fatunla and published by Academic Press. This book was released on 2014-05-10 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Method for Initial Value Problems in Ordinary Differential Equations deals with numerical treatment of special differential equations: stiff, stiff oscillatory, singular, and discontinuous initial value problems, characterized by large Lipschitz constants. The book reviews the difference operators, the theory of interpolation, first integral mean value theorem, and numerical integration algorithms. The text explains the theory of one-step methods, the Euler scheme, the inverse Euler scheme, and also Richardson's extrapolation. The book discusses the general theory of Runge-Kutta processes, including the error estimation, and stepsize selection of the R-K process. The text evaluates the different linear multistep methods such as the explicit linear multistep methods (Adams-Bashforth, 1883), the implicit linear multistep methods (Adams-Moulton scheme, 1926), and the general theory of linear multistep methods. The book also reviews the existing stiff codes based on the implicit/semi-implicit, singly/diagonally implicit Runge-Kutta schemes, the backward differentiation formulas, the second derivative formulas, as well as the related extrapolation processes. The text is intended for undergraduates in mathematics, computer science, or engineering courses, andfor postgraduate students or researchers in related disciplines.

Journal of Computational Mathematics

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Author :
Publisher :
ISBN 13 :
Total Pages : 808 pages
Book Rating : 4.:/5 (35 download)

Book Synopsis Journal of Computational Mathematics by :

Download or read book Journal of Computational Mathematics written by and published by . This book was released on 1983 with total page 808 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Numerical Solution of Nonlinear Stiff Initial Value Problems

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Author : W. H. Hundsdorfer
Publisher :
ISBN 13 :
Total Pages : 158 pages
Book Rating : 4.:/5 (44 download)

Book Synopsis The Numerical Solution of Nonlinear Stiff Initial Value Problems by : W. H. Hundsdorfer

Download or read book The Numerical Solution of Nonlinear Stiff Initial Value Problems written by W. H. Hundsdorfer and published by . This book was released on 1985 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations

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Author : K. E. Brenan
Publisher : SIAM
ISBN 13 : 0898713536
Total Pages : 261 pages
Book Rating : 4.8/5 (987 download)

Book Synopsis Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations by : K. E. Brenan

Download or read book Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations written by K. E. Brenan and published by SIAM. This book was released on 1996-01-01 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes some of the places where differential-algebraic equations (DAE's) occur.

Solving Ordinary Differential Equations I

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Author : Ernst Hairer
Publisher : Springer Science & Business Media
ISBN 13 : 3662126079
Total Pages : 491 pages
Book Rating : 4.6/5 (621 download)

Book Synopsis Solving Ordinary Differential Equations I by : Ernst Hairer

Download or read book Solving Ordinary Differential Equations I written by Ernst Hairer and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: "So far as I remember, I have never seen an Author's Pre face which had any purpose but one - to furnish reasons for the publication of the Book. " (Mark Twain) "Gauss' dictum, "when a building is completed no one should be able to see any trace of the scaffolding," is often used by mathematicians as an excuse for neglecting the motivation behind their own work and the history of their field. For tunately, the opposite sentiment is gaining strength, and numerous asides in this Essay show to which side go my sympathies. " (B. B. Mandelbrot, 1982) 'This gives us a good occasion to work out most of the book until the next year. " (the Authors in a letter, dated c. kt. 29, 1980, to Springer Verlag) There are two volumes, one on non-stiff equations, now finished, the second on stiff equations, in preparation. The first volume has three chapters, one on classical mathematical theory, one on Runge Kutta and extrapolation methods, and one on multistep methods. There is an Appendix containing some Fortran codes which we have written for our numerical examples. Each chapter is divided into sections. Numbers of formulas, theorems, tables and figures are consecutive in each section and indi cate, in addition, the section number, but not the chapter number. Cross references to other chapters are rare and are stated explicitly. The end of a proof is denoted by "QED" (quod erat demonstrandum).

Solving Nonlinear Differential Equations by One-step Methods

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Author : Yili Huang
Publisher :
ISBN 13 :
Total Pages : 154 pages
Book Rating : 4.:/5 (33 download)

Book Synopsis Solving Nonlinear Differential Equations by One-step Methods by : Yili Huang

Download or read book Solving Nonlinear Differential Equations by One-step Methods written by Yili Huang and published by . This book was released on 1993 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:

A Nonlinear Multistep Method for Solving Stiff Initial Value Problems

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Author : Moody Ten-Chao Chu
Publisher :
ISBN 13 :
Total Pages : 180 pages
Book Rating : 4.3/5 (129 download)

Book Synopsis A Nonlinear Multistep Method for Solving Stiff Initial Value Problems by : Moody Ten-Chao Chu

Download or read book A Nonlinear Multistep Method for Solving Stiff Initial Value Problems written by Moody Ten-Chao Chu and published by . This book was released on 1982 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Chinese Journal of Numerical Mathematics and Applications

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Publisher :
ISBN 13 :
Total Pages : 484 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Chinese Journal of Numerical Mathematics and Applications by :

Download or read book Chinese Journal of Numerical Mathematics and Applications written by and published by . This book was released on 1990 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Modern Numerical Methods for Ordinary Differential Equations

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Author : G. Hall
Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 358 pages
Book Rating : 4.:/5 (44 download)

Book Synopsis Modern Numerical Methods for Ordinary Differential Equations by : G. Hall

Download or read book Modern Numerical Methods for Ordinary Differential Equations written by G. Hall and published by Oxford University Press, USA. This book was released on 1976 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Government Reports Announcements & Index

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Publisher :
ISBN 13 :
Total Pages : 960 pages
Book Rating : 4.3/5 (243 download)

Book Synopsis Government Reports Announcements & Index by :

Download or read book Government Reports Announcements & Index written by and published by . This book was released on 1983 with total page 960 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Ordinary Differential Equations

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

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.

Numerical Solution of Ordinary Differential Equations

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Author : L.F. Shampine
Publisher : Routledge
ISBN 13 : 1351427547
Total Pages : 498 pages
Book Rating : 4.3/5 (514 download)

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 498 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.

Solving ODE Initial Value Problems With Implicit Taylor Series Methods

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Publisher :
ISBN 13 :
Total Pages : 116 pages
Book Rating : 4.:/5 (317 download)

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Download or read book Solving ODE Initial Value Problems With Implicit Taylor Series Methods written by and published by . This book was released on 2000 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Solution of Ordinary Differential Equations

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Author : L. Fox
Publisher : Springer Science & Business Media
ISBN 13 : 9400931298
Total Pages : 259 pages
Book Rating : 4.4/5 (9 download)

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

Download or read book Numerical Solution of Ordinary Differential Equations written by L. Fox and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nearly 20 years ago we produced a treatise (of about the same length as this book) entitled Computing methods for scientists and engineers. It was stated that most computation is performed by workers whose mathematical training stopped somewhere short of the 'professional' level, and that some books are therefore needed which use quite simple mathematics but which nevertheless communicate the essence of the 'numerical sense' which is exhibited by the real computing experts and which is surely needed, at least to some extent, by all who use modern computers and modern numerical software. In that book we treated, at no great length, a variety of computational problems in which the material on ordinary differential equations occupied about 50 pages. At that time it was quite common to find books on numerical analysis, with a little on each topic ofthat field, whereas today we are more likely to see similarly-sized books on each major topic: for example on numerical linear algebra, numerical approximation, numerical solution ofordinary differential equations, numerical solution of partial differential equations, and so on. These are needed because our numerical education and software have improved and because our relevant problems exhibit more variety and more difficulty. Ordinary differential equa tions are obvious candidates for such treatment, and the current book is written in this sense.

Numerical Solution of Initial-value Problems in Differential-algebraic Equations

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Author : Kathryn Eleda Brenan
Publisher : North Holland
ISBN 13 :
Total Pages : 232 pages
Book Rating : 4.3/5 (97 download)

Book Synopsis Numerical Solution of Initial-value Problems in Differential-algebraic Equations by : Kathryn Eleda Brenan

Download or read book Numerical Solution of Initial-value Problems in Differential-algebraic Equations written by Kathryn Eleda Brenan and published by North Holland. This book was released on 1989 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: