Open AccessSome features of numerical diagnostics of instantaneous blow-up of the solution by the example of solving the equation of slow diffusion
Author(s) -
Igor V. Prigorniy,
Alexander Anatolyevich Panin,
D. V. Lukyanenko
Publication year - 2021
Publication title -
vyčislitelʹnye metody i programmirovanie
Language(s) - English
Resource type - Journals
eISSN - 1726-3522
pISSN - 0507-5386
DOI - 10.26089/nummet.v22r106
Subject(s) - extrapolation , mathematics , richardson extrapolation , partial differential equation , a priori and a posteriori , boundary value problem , diffusion , diffusion equation , mathematical analysis , scheme (mathematics) , differential equation , ordinary differential equation , physics , philosophy , epistemology , thermodynamics , economy , economics , service (business)
В работе демонстрируется, как метод апостериорной оценки порядка точности разностной схемы по Ричардсону позволяет сделать вывод о некорректности постановки (в смысле отсутствия решения) решаемой численно начально-краевой задачи для уравнения в частных производных. Это актуально в ситуации, когда аналитическое доказательство некорректности постановки ещё не получено или принципиально невозможно. 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.