Frequency-domain analysis of time-integration methods for semidiscrete finite element equations-part I: Parabolic problems

Time-integration for methods for semidiscrete equations emanating from parabolic differential equations are analysed in the frequency domain. The discrete-time transfer functions of three popular methods are derived, and subsequently the forced response characteristics of single modes are studied in the frequency domain. To enable consistent comparison of the frequency responses of different algorithms, three characteristics numbers are identified. Frequency responses and L₂-norms of the phase and magnitude errors are compared for the three time-integration algorithms. The examples demonstrate that frequency-domain analysis provides substantial insight into the time-domain properties of time-integration algorithms.