6 edition of **Stable Recursions With Applications to the Numerical Solution of Stiff Systems (Computational mathematics and applications)** found in the catalog.

Stable Recursions With Applications to the Numerical Solution of Stiff Systems (Computational mathematics and applications)

T. Caspersson

- 178 Want to read
- 8 Currently reading

Published
**June 1980**
by Academic Pr
.

Written in English

- Iterative methods (Mathematics,
- Numerical integration,
- Numerical solutions,
- Differential Equations,
- Stiff computation (Differentia,
- Stiff computation (Differential equations)

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 223 |

ID Numbers | |

Open Library | OL9280714M |

ISBN 10 | 0121630501 |

ISBN 10 | 9780121630508 |

clude important applications in the description of processes with multiple time scales (e.g., fast and slow chemical reactions) and in spatial semi-discretizations of time-dependent partial diﬀeren-tial equations. For example, for the heat equa-tion, stable numerical solutions are obtained with the explicit Euler method only when temporalFile Size: KB. Numerical methods vary in their behavior, and the many different types of differ-ential equation problems affect the performanceof numerical methods in a variety of ways. An excellent book for “real world” examples of solving differential equations is that of Shampine, Gladwell, and Thompson [74].File Size: 1MB.

In numerical ordinary differential equations, various concepts of numerical stability exist, for instance A-stability. They are related to some concept of stability in the dynamical systems sense, often Lyapunov stability. It is important to use a stable method when solving a stiff equation. of numerical algorithms for ODEs and the mathematical analysis of their behaviour, cov-ering the material taught in the in Mathematical Modelling and Scientiﬁc Compu-tation in the eight-lecture course Numerical Solution of Ordinary Diﬀerential Equations. The notes begin with a study of well-posedness of initial value problems for a File Size: KB.

[26] proposed the ADM to solve stiff systems of ordinary differential equations. The reminder of this paper is organized as follows: in the following section the variational iteration method is explained. In Section 3 we propose the solution method and we solve three test problems. The numerical results are proposed in Section 4. 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 small. It 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. When integrating a differential equation numerically.

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Get this from a library. Stable recursions: with applications to the numerical solution of stiff systems. [J R Cash]. Get this from a library. Stable recursions: with applications to the numerical solution of stiff systems.

[J R Cash] -- Chromosome identification: Medicine and Natural Sciences. An algorithm is given for approximating dominated solutions of linear recursions, when some initial conditions are given. The stability of this algorithm is investigated and expressions for the Cited by: REVIEWS AND DESCRIPTIONS OF TABLES AND BOOKS Cash, Stable Recursions, with Applications to the Numerical Solution of Stiff Systems, Academic Press, London, 2.

Wimp, Sequence Transformations and Their Applications, Academic Press, New York, Cash, J.R.: Stable recursions, with applications to the numerical solution of stiff systems. London, New York: Academic Press Google Scholar Ehle, B.L.: High orderA-stable methods for the numerical solution of differential equations.

Comprised of 15 chapters, this book begins with an introduction to high-order A-stable averaging algorithms for stiff differential systems, followed by a discussion on second derivative multistep formulas based on g-splines; numerical integration of linearized stiff ODEs; and numerical solution of large systems of stiff ODEs in a modular simulation framework.

Comprised of 15 chapters, this book begins with an introduction to high-order A-stable averaging algorithms for stiff differential systems, followed by a discussion on second derivative multistep formulas based on g-splines; numerical integration of linearized stiff ODEs; and numerical solution of large systems of stiff ODEs in a modular Book Edition: 1.

A family of recursions, called congruent recursions, is proved to be strongly stable in evaluating its non-negative solutions. A type of strongly unstable recursion is identified. The recursive formula discussed by Panjer () is proved to be strongly stable in evaluating the compound Poisson and the compound Negative Binomial (including Geometric) by: Neural Network for finding approximated solution of stiff differential equations and systems and comparing the result with the analytical–numerical solution of the problems to present general approach for solving stiff equations and systems.

This method uses a feed forward neural network as the basic approximation component. Numerical solutions for stiff ODE systems ()()0Ae B x Q x−+ = () By neglecting and solving the system ofAe B=, the unknown vector e and therefore the coefficient of x2 in () is obtained.

We set (1) y2 =e, then by repeating the above procedure for m iteration, a power series of the following form is File Size: KB. Moreover, these systems are often nonlinear [4]. In the last 40 years or so, numerous works have been focusing on the development of more advanced and e cient methods for sti problems.

A potentially good numerical method for the solution of sti systems of ODEs must have good accuracy and some reasonably wide region of absolute stabil. Cash, Stable recursions, Academic Press [Harcourt Brace Jovanovich, Publishers], London-New York-Toronto, Ont., With applications to the numerical solution of stiff systems; Computational Mathematics and Applications.

MR J. CASH: Stable Recursions; with applications to the numerical solution of stiff systems H. ENGELS: Numerical Quadrature and Cubature L.

DELVES and T. FREEMAN: Analysis of Global Expansion Methods: weakly asymptotically diagonal systems J. AKIN: Application and Implementation of Finite Element Methods. systems is similar to that of stiff linear systems.

In this paper, properties of stiff linear systems are examined prior to a treatment of non-linear equations. Then a few numerical methods are considered. The failure of the usual methods is explained and other methods are described which may be by: This paper is concerned with methods which consist of sequential application of several different schemes for stiff ordinary differential systems, with a predetermined ratio of step-lengths.

We show that, under some conditions, such composite methods have higher order and better stability than the constituent itions of Obrechkoff methods and of implicit Runge–Kutta processes Cited by: 7. Other features include essays, book reviews, case studies from industry, classroom notes, and problems and solutions.

Stable Recursions with Applications to the Numerical Solution of Stiff Systems. The final approximation to the required solution is obtained via a linear combination of asymptotically less Single step exponentially fitted integration formulae of orders 4 and 6 are derived.

On the design of high order exponentially fitted formulae for the numerical integration of stiff systems | Cited by: 6. A class of extended backward differentiation formulae suitable for the approximate numerical integration of stiff systems of first order ordinary differential equations is derived.

An algorithm is described whereby the required solution is predicted using a conventional backward differentiation scheme and then corrected using an extended backward differentiation scheme of higher by: Stability concepts in the numerical solution of difference and differential equations.

Author links open overlay panel J.R. Cash. Show more. J.R. Cash, Stable Recursions, with Applications to the Numerical Solution of Stiff Systems, Academic Press, London, (). J.R. Cash, Two new finite difference schemes for parabolic equations Cited by: 3.

An Introductory Tour. With applications to the numerical solution of stiff systems out one method that has the fourth order of accuracy and is stable for stiff systems with any choice of. Comparison of Stability of Selected Numerical Methods for Solving Stiff Semi-Linear Differential Equations he also presented their application to the numerical solution of the solution of stiff systems.

He presented an implementation of such a scheme to the fully spectral solution of the incompressible magneto hydrodynamic equations in File Size: KB. Numerical Solutions of Stiff Initial Value Problems Using Modified Extended Backward Differentiation Formula T.J. Abdulla, J.R.

Cash, An MEBDF package for the numerical solution of large sparse systems of stiff initial value problems. J.R. Cash, Stable Recursions with Applications to Stiff Differential Equations, Academic Press, London.Most realistic stiff systems do not have analytical solutions so that a numerical procedure must be used.

Computer implementation of such algorithms is widely available e.g. DIFSUB, GEAR, EPISODE etc. The most popular methods for the solution of stiff initial value problems for ordinary differential equations are the backwardCited by: 4.