Numerical Aspects of the Coefficient 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 coecients is necessary. This leads to solve linear systems which can be expressed in dierent 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 dierent formulations. For all the considered cases Vandermonde systems on general abscissae are involved and they are always solved by the Bjork-Pereyra algorithm [3]. An adaptation of the forward error analysis given in [8, 9] is proposed whose signicance is conrmed by the numerical results.