Design of numerical algorithms for the problem of charge transport in a 2D silicon MOSFET transistor with a silicon oxide nanochannel

We are concerned with the problem of charge transport in a 2D silicon MOSFET transistor occupying a domain Ω with a silicon oxide nanochannel occupying a domain ΩG. After proposing an additional boundary condition for the electric potential on the common boundary of the domains Ω and ΩG we design two numerical algorithms for funding approximate solutions of this problem. The first algorithm is a new one and uses interpolation polynomials of spline-collocation and the sweep method. The second algorithm is based on the well-known longitudinal-transverse sweep (l.t.s.) method. By using these algorithms we obtain graphs of stationary solutions of our problem. We also compare the workability and efficiency of the proposed algorithms for various values of parameters.