A comparison of marching-on in time method with marching-on in degree method for the tdie solver

One of the most popular methods to solve a time-domain integral equation (TDIE) is the marching-on in time (MOT) method. Recently, a new method called marching-on in degree (MOD) that uses Laguerre polynomials as temporal basis functions has been developed to eliminate the late time instability of the MOT method. The use of an entire domain basis for the time variable eliminates the requirement of a Courant condition, as there is no time variable involved in the field calculation. This is possible as in the procedure the time and the space variables can be separated analytically. A comparison is presented between these two methods from the standpoint of formulation, stability, cost, and accuracy. Numerical results are presented to illustrate these features in the comparison.