A numerical modelling of the limit problem for the magnetically noninsulated diode

In this paper we consider the initial modelling step dealing with a limit problem of the general PDE system, making the bidimensional parameter dependent boundary ODE system. Since the equation system is singular at initial point t=0 and coincide with Gear's definition of stiff ODE system, we proposed a combined approach for solving the boundary problem and estimation of parameters, complying the given boundary conditions. To do this we use some newly developed derivative free self-convergent methods, which proved themselves to be more numerically stable than a classical Steffensen's method.