An operational matrix-based algorithm for simulating linear and fractional differential circuits

We present a new time-domain simulation algorithm (named OPM) based on operational matrices, which naturally handles system models cast in ordinary differential equations (ODEs), differential algebraic equations (DAEs), high-order differential equations and fractional differential equations (FDEs). When applied to simulating linear systems (represented by ODEs or DAEs), OPM has similar performance to advanced transient analysis methods such as trapezoidal or Gear's method in terms of complexity and accuracy. On the other hand, OPM naturally handles FDEs without much extra effort, which can not be efficiently solved using existing time-domain methods. High-order differential systems, being special cases of FDEs, can also be simulated using OPM. Moreover, adaptive time step can be utilized in OPM to provide a more flexible simulation with low CPU time. Numerical results then validate OPM's wide applicability and superiority.