Numerical Methods That Preserve a Lyapunov Function for Ordinary Differential Equations

Numerical Methods for Ordinary Differential Equations

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 methods for Lyapunov equations

This chapter is about numerical methods for a particular type of equation expressed as a matrix equality. The Lyapunov equation is the most common problem in the class of problems called matrix equations. Other examples of matrix equations: Sylvester equation, Stein equation, Riccati equation. Definition 4.0.1. Consider two square matrices A, W ∈ Rn×n. The problem to find a square matrix X ∈ Rn...

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...

Numerical Analysis and Methods for Ordinary Differential Equations

a numerical method.