A Numerical Integrator for Oscillatory Problems

A Stroboscopic Numerical Method for Highly Oscillatory Problems

We suggest a method for the integration of highly oscillatory systems with a single high frequency. The new method may be seen as a purely numerical way of implementing the analytical technique of stroboscopic averaging. The technique may be easily implemented in combination with standard software and may be applied with variable step sizes. Numerical experiments show that the suggested algorit...

An exponential integrator for a highly oscillatory Vlasov equation

In the framework of a Particle-In-Cell scheme for some 1D Vlasov-Poisson system depending on a small parameter, we propose a time-stepping method which is numerically uniformly accurate when the parameter goes to zero. Based on an exponential time differencing approach, the scheme is able to use large time steps with respect to the typical size of the fast oscillations of the solution.

High Order Numerical Methods for Highly Oscillatory Problems

This paper is concerned with the numerical solution of nonlinear Hamiltonian oscillatory systems of second-order differential equations of a special form. We present numerical methods of high asymptotic as well as time stepping order based on the modulated Fourier expansion of the exact solution. Furthermore, numerical experiments on the modified Fermi-Pasta-Ulam problem support our investigati...

Traveing Salesperson Problems for a double integrator

In this paper we propose some novel path planning strategies for a double integrator with bounded velocity and bounded control inputs. First, we study the following version of the Traveling Salesperson Problem (TSP): given a set of points in R, find the fastest tour over the point set for a double integrator. We first give asymptotic bounds on the time taken to complete such a tour in the worst...

The Electronic Numerical Integrator