TY - JOUR
T1 - Numerical Methods for the Hyperbolic Monge-Ampere Equation Based on the Method of Characteristics
AU - Bertens, Maikel W.M.C.
AU - Vugts, Ellen M.T.
AU - Anthonissen, Martijn J.H.
AU - ten Thije Boonkkamp, Jan H.M.
AU - IJzerman, Wilbert L.
PY - 2021/4
Y1 - 2021/4
N2 - 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-Ampere (MA) equation, for which we solve the system of ODEs using explicit one-step methods (Euler, Runge-Kutta) and spline interpolation. Numerical examples demonstrate the performance of the methods.
AB - 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-Ampere (MA) equation, for which we solve the system of ODEs using explicit one-step methods (Euler, Runge-Kutta) and spline interpolation. Numerical examples demonstrate the performance of the methods.
U2 - 10.48550/arXiv.2104.11659
DO - 10.48550/arXiv.2104.11659
M3 - Article
VL - 2021
JO - arXiv
JF - arXiv
M1 - 2104.11659
ER -