Numerical methods for ordinary differential equations on matrix manifolds

Numerical Methods for Ordinary Differential Equations

Numerical Integration of Ordinary Differential Equations on Manifolds

This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential equations on m...

Parallel Methods for the Numerical Integration of Ordinary Differential Equations

Abstract. In this paper we derive a class of numerical integration formulas of a parallel type for ordinary differential equations. These formulas may be used simultaneously on a set of arithmetic processors to increase the integration speed. Conditions for the convergence of such formulas are formulated. Explicit examples for two and four processor cases are derived. Results of numerical exper...

Parallel Numerical Methods for Ordinary Differential Equations: a Survey

Tremendous efforts have been made in the field of parallel numerical methods for ODE. Special volumes are dedicated to the theme we are going to discuss [1]. The brief survey of some classical results and recent developments is the aim of this paper. We particulary focus on small scale parallelism across the method, but not large scale parallelism across the system.

Numerical Analysis and Methods for Ordinary Differential Equations

a numerical method.