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

Maikel W.M.C. Bertens; Ellen M.T.  Vugts; Martijn J.H. Anthonissen; Jan H.M. ten Thije Boonkkamp; Wilbert L. IJzerman

doi:10.48550/arXiv.2104.11659

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

Maikel W.M.C. Bertens
, Ellen M.T. Vugts
, Martijn J.H. Anthonissen
, Jan H.M. ten Thije Boonkkamp
, Wilbert L. IJzerman

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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 language	English
Article number	2104.11659
Number of pages	43
Journal	arXiv
Volume	2021
DOIs	https://doi.org/10.48550/arXiv.2104.11659
Publication status	Published - Apr 2021

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title = "Numerical Methods for the Hyperbolic Monge-Ampere Equation Based on the Method of Characteristics",

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.",

author = "Bertens, \{Maikel W.M.C.\} and Vugts, \{Ellen M.T.\} and Anthonissen, \{Martijn J.H.\} and \{ten Thije Boonkkamp\}, \{Jan H.M.\} and IJzerman, \{Wilbert L.\}",

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AU - Bertens, Maikel W.M.C.

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AU - Anthonissen, Martijn J.H.

AU - ten Thije Boonkkamp, Jan H.M.

AU - IJzerman, Wilbert L.

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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.

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M3 - Article

VL - 2021

JO - arXiv

JF - arXiv

M1 - 2104.11659

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

Abstract

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