A nonconventional stability approach for a nonlinear Crank–Nicolson method solving degenerate Kawarada problems

Abstract

Conventionally, the numerical stability of finite difference approximations of nonlinear Kawarada problems is shown only via frozen source terms, that is, ignoring potential jeopardization from quenching nonlinearities. The approach leaves an inadequacy behind even in the sense of localized stability analysis. This paper provides a much improved analysis of the numerical stability without freezing nonlinear source terms of the underlying equations. The strategy implemented can be extended for similar endeavors to higher dimensional cases. Simulation experiments are included.