Numerical aspects of the coeffcient computation for LMMs

The numerical solution of Boundary Value Problems usually requires the use of an adaptive mesh selection strategy. For this reason, when a Linear Multistep Method is considered, a dynamic computation of its coefficients is necessary. This leads to solve linear systems which can be expressed in different forms, depending on the polynomial basis used to impose the order conditions. In this paper, we compare the accuracy of the numerically computed coefficients for three different formulations. For all the considered cases Vandermonde systems on general abscissae are involved and they are always solved by the Björk-Pereyra algorithm [3]. An adaptation of the forward error analysis given in [8, 9] is proposed whose significance is confirmed by the numerical results.