A Method for Global Approximation of the Initial Value Problem

For the numerical solution of the initial value problem a parallel, global integration method is derived and studied. It is a collocation method. If f(x,y)≡f(x) the method coincides with the Filippi's modified Clenshaw–Curtis quadrature [11]. Two numerical algorithms are considered and implemented, one of which is the application of the new method to Picard iterations, so it is a waveform relaxation technique [3]. Numerical experiments are favourably compared with the ones given by the known GAM [2], GBS [14] and Sarafyan [18] methods.