Diagnostics of Instant Decomposition of Solution in the Nonlinear Equation of Theory of Waves in Semiconductors

Abstract

The paper considers a method for numerical diagnostics of the solution’s blow-up in a nonlinear equation of the theory of waves in semiconductors. One feature of the problem under consideration is that there is not even a weak local solution to the problem in time on the positive half-line in spatial variable, while there exists a classical solution local in time in the spatial interval from 0 to L. We numerically show that the lifetime of the solution tends to zero as L tends to infinity. The numerical diagnostics of the solution’s blow-up is based on the method of calculating a posterior asymptotically accurate estimate of the error of the obtained numerical solution according to the Richardson extrapolation method.