2021/04/23 by Maikel W. M. C. Bertens, Bertens, Maikel W. M. C., Ellen M. T. Vugts +7 · 1 citation
Mathematics · Physics and Astronomy · #35L70 (primary) #65M25 and 65N22 (secondary) #Advanced Mathematical Physics Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Nonlinear Waves and Solitons #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2104.11659
openalex publication_date 2021/04/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We present three alternative derivations of the method of characteristics\n(MOC) for a second order nonlinear hyperbolic partial differential equation.\nThe MOC gives rise to two mutually coupled systems of ordinary differential\nequations. As a special case we consider the Monge-Amp `ere equation, for which\nwe solve the system of ODE's using explicit one-step methods (Euler,\nRunge-Kutta) and spline interpolation. Numerical examples demonstrate the\nperformance of the methods.\n