A Comparison of Several Methods for Solving Second-Order Damped Systems of Ordinary Differential Equations

Several numerical methods for the solution of a second-order damped system of the form MÜ(t) + 2CŮ(t) + KU(t) = F(t) are compared in this study. Factors considered in the comparison are stability, difficulty and cost of implementation, and accuracy. The methods we consider are Compact Implicit schemes, Central Differences, Wilson's θ-method, Padé approximations on equivalent first-order systems, and methods based on rational approximations to the cosine matrix.

Both conditionally stable and unconditionally stable methods are studied. Problems with high frequency components in the solution are considered. The Padé schemes are evidenced to be particularly effective.