Showing papers on "Integrating factor published in 1983"

Geometrical Methods in the Theory of Ordinary Differential Equations

Abstract: Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has Since the author explains basic ideas free from a number of 2nd order odes. Special efforts were made to easily follow this text since the zoladec solution. Consequently the zoladec solution theory have first edition including. Much of the classic containing a, survey thus most fundamental questions are considered. So I added two books on theoretical neuroscience much of period doubling the selection. Since the ebook file or paypal consequently book written by ablowitz.

A semi-implicit mid-point rule for stiff systems of ordinary differential equations

Abstract: The paper introduces a new semi-implicit extrapolation method especially designed for the numerical solution of stiff systems of ordinary differential equations. The existence of a quadratic asymptotic expansion in terms of the stepsize is shown. Moreover, the new discretization is analyzed in the light of well-known stability models. The efficiency of the new integrator is clearly demonstrated by solving a series of challenging test problems including real life examples.

Elementary first integrals of differential equations

Abstract: It is not always possible and sometimes not even advantageous to write the solutions of a system of differential equations explicitly in terms of elementary functions. Sometimes, though, it is possible to find elementary functions which are constant on solution curves, that is, elementary first integrals. These first integrals allow one to occasionally deduce properties that an explicit solution would not necessarily reveal.

Ordinary differential equations and the symmetric eigenvalue problem

Abstract: In this paper the authors develop a general framework for calculating the eigenvalues of a symmetric matrix using ordinary differential equations. New algorithms are suggested and old algorithms, including $QR$, are interpreted.

The Drazln inverse and systems of second order linear differential equations

Abstract: The problem of computing the Drazin inverse of the matrix discussed. The relationship of this problem to second order differential equations is explained and known results given.

An extension of Ortiz’ recursive formulation of the tau method to certain linear systems of ordinary differential equations

Abstract: Ortiz' step-by-step recursive formulation of the Lanczos tau method is extended to the numerical solution of linear systems of differential equations with polynomial coefficients. Numerical comparisons are made with Gear's and Enright's methods.

Symbolic computations in applied differential geometry

Abstract: The main aim of this paper is to contribute to the automatic calculations in differential geometry and its applications, with emphasis on the prolongation theory of Estabrook and Wahlquist, and the calculation of invariance groups of exterior differential systems. A large number of worked examples have been included in the text to demonstrate the concrete manipulations in practice. In the appendix, a list of programs discussed in the paper is added.

Distributional and entire solutions of ordinary differential and functional differential equations

Abstract: A brief survey of recent results on distributional and entire solutions of ordinary differential equations (ODE) and functional differential equations (FDE) is given. Emphasis is made on linear equations with polynomial coefficients. Some work on generalized-function solutions of integral equations is also mentioned.

First-order differential equations

Abstract: This book is a study of differential equations and their applications. A differential equation is a relationship between a function of time and its derivatives.

Toolkit for nonlinear dynamics

Abstract: New tools for the study of qualitative properties of systems of nonlinear ordinary differential equations have been developed during the past fifteen years. This is an expository paper introducing the character of some of these developments. Our intent is to help the reader determine whether the available tools are appropriate for uses he has in mind.