A: The PSIM algorithm uses nodal analysis with the trapezoidal rule integration. Importantly PSIM solves all equations simultaneously and does not generate state-space matrices which are common in other system level simulators. These state space matrices introduce convergence problems when there are large derivatives.
PSIM is loosely based on EMTP techniques developed by Dr. H. Dommel in his pioneering work on computational methods for solving electromagnetic transients.
With version 11, a SPICE engine based on SPICE 3F5 and NGSPICE was integrated into PSIM. This new SPICE variant is now available as an alternate engine to simulate a circuit.