Performance of a parallel technique for solving nonlinear systems arising from ODEs

An inexact Newton method is commonly used to solve large nonlinear systems, arising for instance from simulating models in mathematics, chemistry and physics. In this paper, we propose an implementation of parallelization across the method in solving a nonlinear system, arising from Runge-Kutta method, which is a part of our work on ODE. We also implement parallelization across the system in solving the arising linear system, with the aim of investigating whether this will contribute to speedup to the whole process. We used two kinds of test problems related to ordinary differential equations (ODEs), i.e. Brusselator and Dense problems. The experiment was performed on a cluster of PCs with PVM message passing environment. Our observation shows that for Brusselator problem, using multiprocessors will result in a better performance in terms of speedup for sufficiently large data. For Dense problem, though we expect to have speedup more than two, the maximum attainable speedup is only two.