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L. Hörmander (2007)
The Analysis of Linear Partial Differential Operators III
(2001)
Comparaison de schemas numériques resolvant l’équation d’advection
Daniel Bouche, G. Bonnaud, D. Ramos (2003)
Comparison of numerical schemes for solving the advection equationAppl. Math. Lett., 16
V. Borovikov (1994)
Uniform Stationary Phase Method
(2004)
Finite Differences Schemes and Partial Differential Equations
(2009)
Uniform stability of Strangs explicit compact schemes for linear advection
O. Vallée, M. Soares (2004)
Airy Functions And Applications To Physics
Y. Shokin (1983)
The Method of Differential Approximation
We analyse the solution of the linear advection equation on a uniform mesh by a non dissipative second order scheme for discontinuous initial condition. These schemes are known to generate parasitic oscillations in the vicinity of the discontinuity. An approximate way to predict these oscillations is provided by the equivalent equation method. More specifically, we focus on the case of advection of a step function by the leapfrog scheme. Numerical experiments show that the equivalent equation method fails to reproduce the oscillations generated by the scheme far from the discontinuity. Thus, we derive closed form exact and approximate solutions for the scheme that accurately predict these oscillations. We study the relationship between equivalent equation approximation and exact solution for the scheme, to determine its range of validity.
Acta Applicandae Mathematicae – Springer Journals
Published: Sep 12, 2013
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