We study the convergence performance of relaxation-based algorithms for circuit sinmlation in the time doraain The circuits are modelled by linem integral-difierential-algebraic equations. We show that in theory convergence depends only on the spectral properties of certain matrices when splitting is applied to the circuit matrices to set up the waveforill relaxation solution of a circuit. A new decoupling technique is derived, which speeds up the convergence of relaxation-based algorithlns. In function spaces a Krylov's subspace method. namely the waveforirl generalized minimal residual algorithm，is also presented in the paper. Nuinerical examples are given to illustrate how judicious splitting mal how Krylov's method Call help improve convergence in sorlle situations.