3 edition of **Numerical solution of initial-value problems in differential-algebraic equations** found in the catalog.

Numerical solution of initial-value problems in differential-algebraic equations

Kathryn Eleda Brenan

- 361 Want to read
- 6 Currently reading

Published
**1989**
by North-Holland in New York
.

Written in English

- Initial value problems -- Numerical solutions.

**Edition Notes**

Includes bibliographical references (p. 189-206).

Statement | K.E. Brenan, S.L. Campbell, L.R. Petzold. |

Contributions | Campbell, S. L., Petzold, Linda Ruth. |

Classifications | |
---|---|

LC Classifications | QA378 .B73 1989 |

The Physical Object | |

Pagination | viii, 210 p. : |

Number of Pages | 210 |

ID Numbers | |

Open Library | OL2197219M |

ISBN 10 | 0444015116 |

LC Control Number | 89016924 |

In mathematics, a stiff equation is a differential equation for which certain numerical methods for solving the equation are numerically unstable, unless the step size is taken to be extremely has proven difficult to formulate a precise definition of stiffness, but the main idea is that the equation includes some terms that can lead to rapid variation in the solution. The physical problem leading to the fractional differential equation () and the numerical solution of the initial-value problem () – () are considered in Section View chapter Purchase book.

Numerical Solution of Ordinary Differential Equations is an excellent textbook for courses on the numerical solution of differential equations at the upper-undergraduate and beginning graduate levels. It also serves as a valuable reference for researchers in the fields of mathematics and engineering. COMPUTATIONAL COMPLEXITY OF NUMERICAL SOLUTIONS OF INITIAL VALUE PROBLEMS FOR DIFFERENTIAL ALGEBRAIC EQUATIONS (Spine title: Computational Complexity of Numerical Solutions of IVP for DAE) (Thesis format: Monograph) by Silvana Ilie Graduate Program in Applied Mathematics Submitted in partial fulﬂllment of the requirements for the degree of.

This book deals with the numerical solution of differential equations, a very important branch of mathematics. initial value problems and boundary value problems, differential algebraic equations, partial differential equations and delay differential equations. The solution of differential equations using R is the main focus of this book. The solution for a differential–algebraic equation can be expanded up to arbitrary order using MAPLE computer algebra systems. First we calculate power series of the given equations system then transform it into Padé series form, which give an arbitrary order for solving differential–algebraic equation numerically.

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Many physical problems are most naturally described by systems of differential and algebraic equations. This book describes some of the places where differential-algebraic equations (DAE's) occur.

The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed. The analysis and numerical solution of boundary value problems for differential-algebraic equations is presented, including multiple shooting and collocation methods.

A survey of current software packages for differential-algebraic equations completes the text. The book is addressed to graduate students and researchers in mathematics Cited by: Many physical problems are most naturally described by systems of differential and algebraic equations.

This book describes some of the places where differential-algebraic equations (DAE's) occur. The basic mathematical theory for these equations is developed and numerical methods are presented and analyzed.

Examples drawn from a variety of applications are used to motivate and. I y(t) is called the solution of the IVP if I y(a) = ; Initial value problems for ordinary differential equations Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs).

A chapter is devoted to index reduction methods that allow the numerical treatment of general differential-algebraic equations.

The analysis and numerical solution of boundary value problems Reviews: 1. On the Numerical Solution of Differential-Algebraic Equations with Hessenberg Index-3 Article (PDF Available) in Discrete Dynamics in Nature and Society (2) September with Reads.

the book discusses methods for solving differential algebraic equations (Chapter 10) and Volterra integral equations (Chapter 12), topics not commonly included in an introductory text on the numerical solution of differential equations.

Numerical Solution of Ordinary Differential Equations presents a complete and easy-to-follow introduction to classical topics in the numerical solution of ordinary differential equations. The book's approach not only explains the presented mathematics, but also helps.

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.

dent variables. NDSolve can also solve some differential-algebraic equations (DAEs), which are typically a mix of differential and algebraic equations. [email protected] 1,eqn 2, numerical solution for the function u with t in the range to t max [email protected] 1,eqn 2.

Numerical methods for ordinary differential equations. Initial value problems. this book has been focused firmly on the solutions of IVPs and how well these are approximated by a variety of.

Home Browse by Title Reports Krylov methods for the numerical solution of initial-value problems in differential-algebraic equations.

Krylov methods for the numerical solution of initial-value problems in differential-algebraic equations December December Read More. Technical Report. Author: Steven L Lee. The initial value problem ential-algebraic equations is equation () along with the initial condition y(iQ) = vq where I is of the form [ig, T].

Numerical methods which can be used to solve D/A systems include Runge Kutta. Additional Physical Format: Online version: Brenan, Kathryn Eleda, Numerical solution of initial-value problems in differential-algebraic equations. In mathematics, a differential-algebraic system of equations (DAEs) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a systems occur as the general form of (systems of) differential equations for vector–valued functions x in one independent variable t, (˙ (), (),) =where: [,] → is a vector of dependent.

Get this from a library. Numerical solution of initial-value problems in differential-algebraic equations. [Kathryn Eleda Brenan; S L Campbell; Linda Ruth Petzold; Society for Industrial and Applied Mathematics.] -- Many physical problems are most naturally described by systems of differential and algebraic equations.

This book describes some of the places where differential-algebraic. for the numerical solution of two-point boundary value problems. Syllabus. Approximation of initial value problems for ordinary diﬀerential equations: one-step methods including the explicit and implicit Euler methods, the trapezium rule method, and Runge–Kutta methods.

Linear multi-step methods: consistency, zero. Numerical Solution of Initial Value Problems. Some of the key concepts associated with the numerical solution of IVPs are the Local Truncation Error, the Order and the Stability of the Numerical Method.

We should also be able to distinguish explicit techniques from implicit ones. In the following, these concepts will be introduced through. Purchase Numerical Methods for Initial Value Problems in Ordinary Differential Equations - 1st Edition.

Print Book & E-Book. ISBNThis book deals with the numerical solution of differential equations, a very important branch of mathematics. Our aim is to give a practical and theoretical account of how to solve a large variety of differential equations, comprising ordinary differential equations, initial value problems and boundary value problems, differential algebraic.

In general, a system of ordinary differential equations (ODEs) can be expressed in the normal form, x^\[Prime](t)=f(t,x) The derivatives of the dependent variables x are expressed explicitly in terms of the independent transient variable t and the dependent variables x.

As long as the function f has sufficient continuity, a unique solution can always be found for an initial value problem where.DOI: / Corpus ID: Numerical solution of initial-value problems in differential-algebraic equations @inproceedings{BrenanNumericalSO, title={Numerical solution of initial-value problems in differential-algebraic equations}, author={Kathryn E.

Brenan and Stephen L. Campbell and Linda R. Petzold}, booktitle={Classics in applied mathematics}, year={} }.Scientific computing with ordinary differential equations. Springer Science & Business Media.

Shampine, L. F. (). Numerical solution of ordinary differential equations. Routledge. Dormand, John R. (), Numerical Methods for Differential Equations: A .