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

Abstract

To verify the solution of a typical Crocco boundary problem, a numerical experiment was performed using an implicit second-order difference scheme. It is shown that a numerical solution approximates a weak solution of a typical Crocco limit problem, except for the right end of the integration interval.The convergence in itself of iterative procedures for numerical solution ensures convergence to a weak solution of the typical Crocco limit problem. Calculation errors at the right end of the integration gap can be reduced by switching to high-order differences.

Keywords

• crocco's typical boundary problem
• implicit difference scheme
• weak solution
• homotopy