Numerical verification of weak solutions of the Crocco typical boundary problem using an implicit second order difference scheme

To verify the solution of a typical Crocco boundary problem, a numerical experiment has been performed using an implicit second-order difference scheme. The computational experiment showed uniform convergence in the 0 ≤ х ≤ 1 interval for the numerical approximation of the solution to a weak solution with a small interval discrete sampling (of the order of N = 104 nodes). It was shown that a numerical solution approximated a weak solution of the typical Crocco limit problem, except for the right end of the integration interval. The solution of the Crocco boundary problem could be continued to the left of the point x = x0 while preserving the continuity and smoothness of the solution at this point. The point x = 1 represents the natural upper bound of the solution domain.