An introduction to ordinary differential equations by computer algebra-systems

We report on an elementary course in ordinary differential equations (odes) for students in engineering sciences. The course is also intended to become a self-study package for odes and is is based on several interactive computer lessons using REDUCE and MATHEMATICA . The aim of the course is not to do Computer Algebra (CA) by example or to use it for doing classroom examples. The aim ist to teach and to learn mathematics by using CA-systems.

Ordinary Differential Equations

Exercises and solutions about ordinary differential equations.

Ordinary fractional differential equations are in fact usual entire ordinary differential equations on time scales

Despite the huge number of works considering fractional derivatives or derivatives on time scales some basic facts remain to be evaluated. Here we will be showing that the fractional derivative of monomials is in fact an entire derivative considered on an appropriate time scale.

Boundedness of solutions of retarded functional differential equations with variable impulses via generalized ordinary differential equations

In this paper, we give sufficient conditions for the uniform boundedness and uniform ultimate boundedness of solutions of a class of retarded functional differential equations with impulse effects acting on variable times. We employ the theory of generalized ordinary differential equations to obtain our results. As an example, we investigate the boundedness of the solution of a circulating fuel nuclear reactor model.

Contractive-like mapping principles in ordered metric spaces and application to ordinary differential equations

[EN] The purpose of this paper is to present a fixed point theorem for generalized contractions in partially ordered complete metric spaces. We also present an application to first-order ordinary differential equations.

Differential invariants of second-order ordinary differential equations

The notion of a differential invariant for systems of second-order differential equations on a manifold M with respect to the group of vertical automorphisms of the projection is de?ned and the Chern connection attached to a SODE allows one to determine a basis for second-order differential invariants of a SODE.

Efficient algorithms for solving systems of ordinary differential equations for ecosystems modeling /

Mode of access: Internet.

An automatic integrator for ordinary differential equations for ILLIAC IV /

"June 1, 1969."

Numerical solution of stiff ordinary differential equations using collocation methods /

Bibliography: p. 79-80.

A computer graphic technique for finding numerical methods for ordinary differential equations.

On cover: COO-1469-0106.

High order stiffly stable methods for ordinary differential equations

Supported in part by contract U.S. AEC AT(11-1) 1469 and in part by National Science Foundation grant NSF-GJ-217.

Multi-derivative numerical methods for the solution of stiff ordinary differential equations /

"Under contracts US AEC AT(11-1)2383 and US AEC AT(11-1)1469."

1979 SIGNUM Meeting on Numerical Ordinary Differential Equations, April 3-5, 1979, University Inn, Champaign, Illinois : jointly sponsored by Association for Computing Machinery, Special Interest Group on Numerical Mathematics; Department of Computer Science, University of Illinois at Urbana-Champaign; National Science Foundation /

Includes bibliographical references.

An efficient numerical method for highly oscillatory ordinary differential equations /

"Supported in part by the Department of Energy under contract ENERGY/EY-76-S-02-2383, and submitted in partial fulfillment of the requirements of the Graduate College for the degree of doctor of philosophy."