This work presents a study on dynamics of a circuit with a non-linear coil, where loss in iron is also taken into account. A coil model is derived using a state space description. The work also includes the development of an application in C# for coil dynamics examination, where the implicit RADAU IIA method of various orders is applied for the purpose of solving non-linear differential equations modelling the non-linear coil with loss in iron.

The paper presents an approach to differential equation solutions for the stiff problem. The method of using the classic transformer model to study nonlinear steady states and to determine the current pulses appearing when the transformer is turned on is given. Moreover, the stiffness of nonlinear ordinary differential state equations has to be considered. This paper compares Runge–Kutta implicit methods for the solution of this stiff problem.