Modeling helps the designer to get a correct understanding of the variables in the system and to make the final hardware accurately. This article presents a mathematical numerical method based on recursive differential equations to calculate voltage and current harmonics, which can be applied to converters that have semiconductor switches with line commutation, such as thyristor, triac, diode, Dyak, Gto, Sith, etc. The characteristic curves of these switches are all non-linear, so they cannot be modeled with conventional linear methods. In the proposed method, the characteristic curve of the switch is first considered, and then the current-voltage relational diagram of the switch is extracted. Then the impedance and transfer matrices related to the linear elements are determined by the method of mesh and knot theory. Then, the block diagram of the converter system, which includes differential operators, is determined. In converters with line commutation, the key fire angle is known and the main problem is that the off angle is dependent on the circuit conditions at any moment. Here, by applying the recursive differential calculation method based on the multivariable Rang-Kottai equation, the instantaneous values of the converter parameters are calculated. After performing the calculations, the off angle of the keys is determined and after that the range of harmonics can be determined up to the desired component and the final numerical model is extracted. Finally, the simulation results have been compared with the proposed analytical-algebraic method, which shows the efficiency of this method in estimating the voltage and current of switches. پرونده مقاله