Various closeness concepts in numerical ODE's

Numerical Solution of ODEs with Distributed Maple

Numerical integration of ODEs with Preisach nonlinearity

In this article we discuss applications of the numerical integration methods to the ordinary differential equations with the Preisach nonlinearity. We use a canonical model of the iron pendulum in the magnetic field as an example of the technique. In particular we use guaranteed estimates of the integration error to rigorously prove the chaotic behaviour of the system considered. MSC 2000: Prim...

NUMERICAL SOLUTIONS OF ODEs USING VOLTERRA SERIES

We propose a numerical approach for solving systems of nonautonomous ordinary differential equations under suitable assumptions. This approach is based on expansion of the solutions by Volterra series and allows to estimate the accuracy of the approximation. Also we can solve some ordinary differential equations for which the classical numerical methods fail.

Multirate Numerical Integration for Stiff ODEs

This paper contains an overview of a self-adjusting multirate method. A simple extension which allows the improvement of the efficiency of the method is introduced. The performance of the extended and the original method is compared for a test problem.

Adaptivity and computational complexity in the numerical solution of ODEs

In this paper we analyze the problem of adaptivity for one-step numerical methods for solving ODEs, both IVPs and BVPs, with a view to generating grids of minimal computational cost for which the local error is below a prescribed tolerance (optimal grids). The grids are generated by introducing an auxiliary independent variable τ and finding a grid deformation map, t = Θ(τ), that maps an equidi...