Parallel Methods for the Numerical Integration of Ordinary Differential Equations

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.

The numerical integration of ordinary differential equations

A reliable efficient general-purpose method for automatic digital computer integration of systems of ordinary differential equations is described. The method operates with the current values of the higher derivatives of a polynomial approximating the solution. It is thoroughly stable under all circumstances, incorporates automatic starting and automatic choice and revision of elementary interva...

Multirate Numerical Integration for Ordinary Differential Equations

Subject headings: Multirate time stepping / Local time stepping / Ordinary differential equations / Stiff differential equations / Asymptotic stability / High-order Rosenbrock methods / Partitioned Runge-Kutta methods / Mono-tonicity / TVD / Stability / Convergence. Het onderzoek dat tot dit proefschrift heeft geleid werd mede mogelijk gemaakt door een Peter Paul Peterichbeurs –verstrekt door d...

Numerical Methods for Ordinary Differential Equations