An alternate method to the alternating time-frequency method

A variational approach is developed which permits the calculation of the steady-state time domain response of nonlinear ordinary differential equations (ODE). Unlike numerical integration, transient calculations are avoided and unlike harmonic balance, all calculations are performed in a single domain, namely the time domain. The relationships are established between the developed method and existing techniques such as finite element in time (FET), standard finite differences (FD) and the harmonic balance method (HBM). The proposed technique also includes an arclength continuation algorithm allowing efficient parametric studies to be performed. Local stability of the solutions is also assessed.