Numerical study of hyperbolic equations with integral constraints arising in semiconductor theory (Q2706408)

The authors consider the following problem NEWLINE\[NEWLINE \frac {\partial ^{2} E}{\partial x \partial t} + A(E, J) \frac {\partial E}{\partial t} + B(E, J) \frac {\partial E}{\partial x} + C(E, J) \frac {\partial J}{\partial t} + D(E, J) = 0, \quad x \in (0, L),\;t > 0,NEWLINE\]NEWLINE NEWLINE\[NEWLINEE(x, 0) = E_{0} (x), \quad x \in (0, L),NEWLINE\]NEWLINE NEWLINE\[NEWLINEE(0, t)=J(t) \rho ,\quad t \geq 0,NEWLINE\]NEWLINE NEWLINE\[NEWLINE\int_{0}^{L} E(x, t) dx = \Phi \in \mathbb{R}^{+},\quad t \geq 0,NEWLINE\]NEWLINE where \(A, B, C\) and \(D\) are known functions. This problem is used to model the Gunn effect in semiconductors with impurity capture. The authors construct on homogeneous grid on time and space the implicit two-point scheme to compute the approximate solution. Stability and convergence have been analized. The results of computation are presented.