A Recursive Method for Calculation of Collocation Constants in Orthogonal Collocation Method

An efficient method for calculation of collocation constants in the orthogonal collocation method was discussed. To make it possible to calculate the collocation constants of arbitrary order using the same subroutine, an algorithm utilizing their recursive properties was proposed. The first and second-order collocation constants calculated based on the algorithm were confirmed to have the same high accuracies as those by the method previously reported. From the result of investigation on accuracies of the approximate values to high-order derivatives of a trigonometric function, the proposed algorithm was shown to also be useful in the calculation of higher-order collocation constants. The execution time required to calculate a set of collocation constants was almost the same as that of the previous method.