Collocation methods with controllable dissipation for linear dynamics

摘要

This paper introduces a unified set of collocation methods for linear dynamics in which a parameter is used to control the position of the collocation points. In this manner, both A-stable algorithms of order 2p and L-stable algorithms of order 2p - 1 are derived from collocation polynomials of degree p. In addition, algorithms with intermediate accuracy and stability properties are made available. The effects of varying the algorithmic parameter are investigated with particular reference to the numerical dissipation of spurious high-frequency modes. Numerical tests are reported which support the theoretical analysis and demonstrate the performance of the proposed algorithms.