Parallel linear system solvers for Runge-Kutta methods (Q1371967)

When solving ordinary differential equations by implicit Runge-Kutta methods, it is often the solution of the arising linear system (from a modified Newton process) which is the most computational intensive part. This paper presents a method which makes it possible to achieve small scale parallelism in the solution of this system by splitting it into subsystems corresponding to each stage of the underlying Runge-Kutta formulae. The drawback of this approach is that it introduces an additional iteration, but nevertheless a speed-up of more than 3 has been achieved on a 4 processor system in comparison to the RADAU5 code.