Some features of numerical diagnostics of instantaneous blow-up of the solution by the example of solving the equation of slow diffusion
Keywords:partial differential equations, numerical diagnostics of the solution’s blow-up, instantaneous blow-up, ill-posed problems
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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