Programming & Computer Software

Diagnostics of instant decomposition of solution in the nonlinear equation of theory of waves in semiconductors

M. O. Korpusov, A. K. Matveeva, D. V. Lukyanenko

Lomonosov Moscow State University, Moscow, Russian Federation

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.

Keywords: numerical diagnostics of instantaneous solution's blow-up.

UDC: 519.6

MSC: 35Q60, 65L12, 74H35

Received: 15.07.2019

DOI: 10.14529/mmp190408