DOI: https://doi.org/10.26089/NumMet.v22r106

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

Authors

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

Keywords:

partial differential equations
numerical diagnostics of the solution’s blow-up
instantaneous blow-up
ill-posed problems

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.

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Published

2021-03-21

Issue

Vol. 22 (2021): Issue 1.

Section

Methods and algorithms of computational mathematics and their applications

Author Biographies

I.V. Prigorniy

Lomonosov Moscow State University,
Faculty of Physics
• Student

A.A. Panin

Lomonosov Moscow State University,
Faculty of Physics
• Associate Professor

D.V. Lukyanenko

Lomonosov Moscow State University,
Faculty of Physics
• Associate Professor

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