A simple ODE solver based on 2-stage Radau IIA (Q1372091)

An initial value problem for an ordinary differential equation (ODE) and its solution via the third-order 2-stage Radau IIA method are presented. The obtained system of nonlinear equations has to be solved usually by a modified Newton process. Several attempts to reduce the LU-costs are briefly described and one new approach with an efficient solver that needs only one LU-decomposition of the dimension of the problem per time step is described. A comparison of the convergence behaviour of this approach with previous ones is presented.