128 citations · 592 across the 51 of their papers we have counts for
3 papers · 2 filters
Butcher series: A story of rooted trees and numerical methods for evolution equations
Robert I McLachlan, Klas Modin, Hans Munthe-Kaas +1
Butcher series appear when Runge-Kutta methods for ordinary differential equations are expanded in power series of the step size parameter. Each term in a Butcher series consists o…
Travelling wave solutions of multisymplectic discretizations of semi-linear wave equations
Fleur McDonald, Robert I McLachlan, Brian E Moore +1
How well do multisymplectic discretisations preserve travelling wave solutions? To answer this question, the 5-point central difference scheme is applied to the semi-linear wave eq…
Discretization of polynomial vector fields by polarization
Elena Celledoni, Robert I. McLachlan, David I. McLaren +2
A novel integration method for quadratic vector fields was introduced by Kahan in 1993. Subsequently, it was shown that Kahan's method preserves a (modified) measure and energy whe…