Roland Haas <rhaas@caltech.edu>

February 12 2014


This thorn provides tests (partially correctness tests) for MoL. It integrates a known function in time choosing for each ODE method a polynomial in time that can be exactly integrated by the method.

1 Introduction

The method of lines thorn (MoL) provides time integration facilities in Cactus. It basically is a wrapper for ODE integrators. As such it can be tested by comparing its results against known analytic solutions.

2 Physical System

For grid functions we integrate

= 1 + tn (1)

where n is chosen such that a given ODE method can integrate the polynomial exactly, eg. n = 3 for the classical Runge-Kutta method. For multi-rate ODE methods, the slow sector integrates

= 1 + 1 4tm (2)

where m is usually smaller than n, eg. 2 for the RK4-RK2 scheme. Finally grid arrays integrate

= 1 + 1 2tn (3)