Numerical results for a parallel linearly-implicit Runge-Kutta method (Q1377293)

This paper considers the stage parallelisation of linearly-implicit Runge-Kutta methods based on restricted Padé approximants with a single (multiple) real pole. Methods of order five are constructed and a parallel implementation on three processors of a distributed memory Parsytec machine is compared with a simple parallelisation of Radau 5 and a diagonally implicit iteration scheme based on Radau 5. Numerical results suggest that for moderately sized problems with a slowly varying Jacobian and at moderate tolerance the linearly implicit implementation compares favourably with the other two approaches.