We consider high-order compact (HOC) schemes for quasilinear parabolic partial differential equations to discretise the Black-Scholes PDE for the numerical pricing of European and American options. We show that for the heat equation with smooth initial conditions, the HOC schemes attain clear fourth
Numerical simulation of 2D square driven cavity using fourth-order compact finite difference schemes
โ Scribed by Jun Zhang
- Book ID
- 104352522
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 699 KB
- Volume
- 45
- Category
- Article
- ISSN
- 0898-1221
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โฆ Synopsis
Fourth-order compact finite difference schemes are employed with multigrid techniques to simulate the two-dimensional square driven cavity flow with small to large Reynolds numbers The governing Navier-Stokes equation is lineaxized in streamfunction and vorticity formulation. The fourth-order compact approximation schemes are coupled with fourth-order approximations for velocities and vorticity boundaries. Numerical solutions axe obtained for square driven cavity flow at high Reynolds numbers and are compared with solutions obtained by other researchers using other approximation methods. (~) 2003 Elsevier Science Ltd. All rights reserved.
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