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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     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},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2021_22_1_a3/}
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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/