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

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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-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.
Original languageEnglish
Number of pages43
JournalarXiv
Volume2021
Issue number2104.11659[math.NA]
Publication statusPublished - Apr 2021

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