Numerical solution and stability analysis for a class of nonlinear differential equations. (English) Zbl 1528.65049
Summary: In this paper, one-dimensional Burgers equation and one-dimensional Laval nozzle flow Euler equation are numerically solved, and the stability of the numerical solutions is analyzed theoretically. In order to satisfy the stability of the numerical solution, the explicit MacCormack scheme is used to obtain the stable solution of the computer numerical simulation. In addition, the numerical and analytical solutions of the Euler equation for one-dimensional Laval nozzle flow are compared, and the results are completely consistent, which verifies the correctness of the numerical solution.
MSC:
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 35Q31 | Euler equations |
| 35Q35 | PDEs in connection with fluid mechanics |
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