Numerical Methods for the Hyperbolic Monge-Amp\`ere Equation Based on the Method of Characteristics
Numerical Analysis
2021-04-26 v1 Numerical Analysis
Abstract
We present three alternative derivations of the method of characteristics (MOC) for a second order nonlinear hyperbolic partial differential equation. The MOC gives rise to two mutually coupled systems of ordinary differential equations. As a special case we consider the Monge-Amp\`ere equation, for which we solve the system of ODE's using explicit one-step methods (Euler, Runge-Kutta) and spline interpolation. Numerical examples demonstrate the performance of the methods.
Cite
@article{arxiv.2104.11659,
title = {Numerical Methods for the Hyperbolic Monge-Amp\`ere Equation Based on the Method of Characteristics},
author = {Maikel W. M. C. Bertens and Ellen M. T. Vugts and Martijn J. H. Anthonissen and Jan H. M. ten Thije Boonkkamp and Wilbert L. IJzerman},
journal= {arXiv preprint arXiv:2104.11659},
year = {2021}
}
Comments
43 pages, 29 figures