A non-standard finite difference scheme for convection in a porous cavity

Moaddy, K.; Hashim, Ishak; Saleh, Habibis

doi:10.1080/10236198.2010.510138

Cited by 2 publications

(1 citation statement)

References 26 publications

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“…In particular, we propose a method that use an exact difference scheme on the linear term and the spatial derivative is approximated using a nonstandard finite difference scheme [7][8][9]. This methodology or similar have been applied in many areas of sciences including biology and epidemic models [7,[10][11][12]. Our aim is to obtain numerical solutions that preserve the positivity as well as stability and consistence.…”

Section: Introductionmentioning

confidence: 99%

Positive numerical solution for a nonarbitrage liquidity model using nonstandard finite difference schemes

González-Parra

Arenasm

Chen-Charpentier

2013

Numerical Methods Partial

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In this article, we construct a numerical method based on a nonstandard finite difference scheme to solve numerically a nonarbitrage liquidity model with observable parameters for derivatives. This nonlinear model considers that the parameters involved are observable from order book data. The proposed numerical method use a exact difference scheme in the linear convection‐reaction term, and the spatial derivative is approximated using a nonstandard finite difference scheme. It is shown that the proposed numerical scheme preserves the positivity as well as stability and consistence. To illustrate the accuracy of the method, the numerical results are compared with those produced by other methods. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 210‐221, 2014

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