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

摘要

We consider a modelling problem of the plane vacuum diode in the magnetic field in the statement by Ben Abdallah et al. [Asymptot. Anal. 20 (1999) 97]. This problem was finally set by a physicists in late 80s and was attentively studied by a number of the mathematicians in 90s. Up to this moment the parameter dependent boundary PDE system has been partially investigated mainly in qualitative aspects. No one complete numerical modelling experiments were made.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.