Geodesic
Some features of numerical diagnostics of instantaneous blow-up of the solution by the example of solving the equation of slow diffusion
Numerical methods and programming, Tome 22 (2021) no. 1, pp. 77-86.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{VMP_2021_22_1_a3,
     author = {I. V. Prigorniy and A. A. Panin and D. V. Lukyanenko},
     title = {Some features of numerical diagnostics of instantaneous blow-up of the solution by the example of solving the equation of slow diffusion},
     journal = {Numerical methods and programming},
     pages = {77--86},
     publisher = {mathdoc},
     volume = {22},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2021_22_1_a3/}
}
TY  - JOUR
AU  - I. V. Prigorniy
AU  - A. A. Panin
AU  - D. V. Lukyanenko
TI  - Some features of numerical diagnostics of instantaneous blow-up of the solution by the example of solving the equation of slow diffusion
JO  - Numerical methods and programming
PY  - 2021
SP  - 77
EP  - 86
VL  - 22
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMP_2021_22_1_a3/
LA  - ru
ID  - VMP_2021_22_1_a3
ER  - 
%0 Journal Article
%A I. V. Prigorniy
%A A. A. Panin
%A D. V. Lukyanenko
%T Some features of numerical diagnostics of instantaneous blow-up of the solution by the example of solving the equation of slow diffusion
%J Numerical methods and programming
%D 2021
%P 77-86
%V 22
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMP_2021_22_1_a3/
%G ru
%F VMP_2021_22_1_a3
I. V. Prigorniy; A. A. Panin; D. V. Lukyanenko. Some features of numerical diagnostics of instantaneous blow-up of the solution by the example of solving the equation of slow diffusion. Numerical methods and programming, Tome 22 (2021) no. 1, pp. 77-86. http://geodesic.mathdoc.fr/item/VMP_2021_22_1_a3/