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

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

Research output: Contribution to journal › Article › Academic

1 Downloads (Pure)

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
Number of pages	43
Journal	arXiv
Volume	2021
Issue number	2104.11659[math.NA]
Publication status	Published - Apr 2021

Access to Document

arXivpaper

Fingerprint Dive into the research topics of 'Numerical Methods for the Hyperbolic Monge-Ampere Equation Based on the Method of Characteristics'. Together they form a unique fingerprint.

Cite this

@article{6175a4aa49db42388deecce9d41e64c4,

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.}",

year = "2021",

month = apr,

language = "English",

volume = "2021",

journal = "arXiv",

publisher = "Cornell University Library",

number = "2104.11659[math.NA]",

}

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.

M3 - Article

VL - 2021

JO - arXiv

JF - arXiv

IS - 2104.11659[math.NA]

ER -