The Stability Analysis of a Class of Numerical Schemes for Partial Differential Systems

The stability analysis of the solutions of the one-dimensional Burgers' equation and the one-dimensional Laval nozzle flow Euler equations are investigated in this paper. To satisfy the stability of the premise condition, the methods for solving these two equations are based on the explicit MacCormack's scheme. Then the stable solutions are obtained through the computer numerical simulation. In addition, in the one-dimensional Laval nozzle flow Euler equation, we compared its numerical solutions and its analytical solutions, the fully consistent results are found.