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Displaying similar documents to “A family of sixth-order compact finite-difference schemes for the three-dimensional Poisson equation.”

An analysis of the influence of data extrema on some first and second order central approximations of hyperbolic conservation laws

Michael Breuss (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We discuss the occurrence of oscillations when using central schemes of the Lax-Friedrichs type (LFt), Rusanov's method and the staggered and non-staggered second order Nessyahu-Tadmor (NT) schemes. Although these schemes are monotone or TVD, respectively, oscillations may be introduced at local data extrema. The dependence of oscillatory properties on the numerical viscosity coefficient is investigated rigorously for the LFt schemes, illuminating also the properties of Rusanov's...

Nonstandard Finite Difference Schemes with Application to Finance: Option Pricing

Milev, Mariyan, Tagliani, Aldo (2010)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 65M06, 65M12. The paper is devoted to pricing options characterized by discontinuities in the initial conditions of the respective Black-Scholes partial differential equation. Finite difference schemes are examined to highlight how discontinuities can generate numerical drawbacks such as spurious oscillations. We analyze the drawbacks of the Crank-Nicolson scheme that is most frequently used numerical method in Finance because of its...

A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems

Thierry Gallouët, Jean-Marc Hérard, Nicolas Seguin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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The present paper is devoted to the computation of single phase or two phase flows using the single-fluid approach. Governing equations rely on Euler equations which may be supplemented by conservation laws for mass species. Emphasis is given on numerical modelling with help of Godunov scheme or an approximate form of Godunov scheme called VFRoe-ncv based on velocity and pressure variables. Three distinct classes of closure laws to express the internal energy in terms of pressure,...

Second-order MUSCL schemes based on Dual Mesh Gradient Reconstruction (DMGR)

Christophe Berthon, Yves Coudière, Vivien Desveaux (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We discuss new MUSCL reconstructions to approximate the solutions of hyperbolic systems of conservations laws on 2D unstructured meshes. To address such an issue, we write two MUSCL schemes on two overlapping meshes. A gradient reconstruction procedure is next defined by involving both approximations coming from each MUSCL scheme. This process increases the number of numerical unknowns, but it allows to reconstruct very accurate gradients. Moreover a particular attention is paid on the...