Methods and algorithms of computational mathematics and their applications

Some features of numerical diagnostics of instantaneous blow-up of the solution by the example of solving the equation of slow diffusion

I. V. Prigorniy, A. A. Panin, D. V. Lukyanenko

Faculty of Physics, Lomonosov Moscow State University

Abstract: The paper demonstrates how the method of a posteriori estimation of the order of accuracy for the difference scheme according to the Richardson extrapolation method allows one to conclude that the formulation of the numerically solved initial-boundary value problem for a partial differential equation is ill-posed (in the sense of the absence of a solution). This is important in a situation when the ill-posedness of the formulation is not analytically proved yet or cannot be proved in principle.

Keywords: partial differential equations; numerical diagnostics of the solution's blow-up; instantaneous blow-up; ill-posed problems.

UDC: 519.6

Received: 30.01.2021

DOI: 10.26089/NumMet.v22r106