Numerical Methods for the Hyperbolic Monge-Ampère Equation Based on the Method of Characteristics

04/23/2021
by   Maikel W. M. C. Bertens, et al.
0

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-Ampère 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.

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