Numerical Methods for Ordinary Differential Equations: Initial Value Problems
- ISBN-10
- 0857291483
- ISBN-13
- 9780857291486
- Series
- Numerical Methods for Ordinary Differential Equations
- Category
- Mathematics
- Pages
- 271
- Language
- English
- Published
- 2010-11-11
- Publisher
- Springer Science & Business Media
- Authors
- David F. Griffiths, Desmond J. Higham
Description
Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject. It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples. Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors. The book covers key foundation topics: o Taylor series methods o Runge--Kutta methods o Linear multistep methods o Convergence o Stability and a range of modern themes: o Adaptive stepsize selection o Long term dynamics o Modified equations o Geometric integration o Stochastic differential equations The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com
Get the book
Other editions
-
- 2016-08-29
- 546 pages
- Paperback
- John Wiley & Sons
-
- 2010-11-25
- 271 pages
- Paperback
- Springer
Similar books
-
Numerical Methods for Ordinary Differential Equations
By J. C. Butcher... 65, 66, 72, 105, 151, 153, 181, 292, 308, 317, 319, 377, 401 estimation, 85, 184, 374, 393 per step, 293 per unit step, 293, 294 rounding, 74 Euler L., 45 existence and uniqueness, 23 Fehlberg E., 181, 191 Feng Kang, xiii finger, ...
-
Numerical Solution of Ordinary Differential Equations
By David E. Stewart, Kendall Atkinson, Weimin HanJ. Baumgarte. “Stabilization of constraints and integrals of motion in dynamical systems”, Computer Methods in Applied Mechanics and ... J.C. Butcher. “Implicit Runge-Kutta processes”, Math. Comp. 18 (1964), pp. 50-64. J .C. Butcher.
-
Numerical Methods for Differential Equations: A Computational Approach
By J.R. DormandThis is a valuable text for students, who will find the derivations of the numerical methods extremely helpful and the programs themselves easy to use.
-
Numerical Quadrature and Solution of Ordinary Differential Equations: A Textbook for a Beginning Course in Numerical Analysis
By A.H. StroudThis is a textbook for a one semester course on numerical analysis for senior undergraduate or beginning graduate students with no previous knowledge of the subject.
-
A First Course in the Numerical Analysis of Differential Equations
By A. IserlesThere exist a number of good introductory texts on multigrid techniques, e.g. Briggs (1987); Hackbusch (1985) and Wesseling (1992). Convergence and complexity (in the ... Briggs, W.L. (1987), A Multigrid Tutorial, SIAM, Philadelphia.
-
Numerical Methods for Ordinary Differential Equations: Proceedings of the Workshop held in L'Aquila (Italy), September 16-18, 1987
By Alfredo Bellen, Charles W. Gear, Elvira RussoDevelopments in numerical initial value ode methods were the focal topic of the meeting at L'Aquila which explord the connections between the classical background and new research areas such as differental-algebraic equations, delay ...
-
Numerical Methods for Initial Value Problems in Ordinary Differential Equations
By Simeon Ola FatunlaThe text is intended for undergraduates in mathematics, computer science, or engineering courses, andfor postgraduate students or researchers in related disciplines.
-
The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods
By J. C. ButcherA step-by-step treatment of differential equations and their solution via numerical methods. Begining by examining differential calculus on a vector space, graphs, and combinatorics then looks at numerical methods for...
-
Numerical Solution of Ordinary Differential Equations
By L.F. ShampineThis new work is an introduction to the numerical solution of the initial value problem for a system of ordinary differential equations.
-
Introduction to Numerical Methods in Differential Equations
By Mark H. HolmesThis book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations.