Abstract
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.
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Costabile, F., Napoli, A. A Method for Global Approximation of the Initial Value Problem. Numerical Algorithms 27, 119–130 (2001). https://doi.org/10.1023/A:1011866317159
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DOI: https://doi.org/10.1023/A:1011866317159