Numerical testing of the stability of viscous shock waves (Q2719066)

The author develops a computer program which evaluates a criterion which is suitable for rapid determination of stability of all types of viscous shock waves. A new theoretical condition on the Evans function is used which serves as a basis for a numerical test of viscous shock wave stability. In fact this condition reduces the question of stability to counting zeros of the analytic Evans function. NEWLINENEWLINENEWLINEAccuracy of the method is demonstrated through a comparison against exact solutions and through a convergence study. The author is able to apply his computational approach even to cases for which no analytical results are known, which illustrates the robustness of the approach. In order to obtain stability of the numerical approximation theoretical results from the Evans function theory are used.