Explicit three-point three-level FDMS for the one-dimensional constant-coefficient advection-diffusion equation
✍ Scribed by J.B. Nixon; B.J. Noye
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 751 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0898-1221
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✦ Synopsis
Two highly stable explicit three-point three-level finite difference methods for the onedimenaionnl constant-coefflclent advection-ditfusion equation are described. These are developed using differencing on a (1,3,1) computational stencil. One is conditionally stable with second-order accuracy, the other is conditionally stable with third-order accuracy. Both are free of numerical ~on.
The two methods are compared, theoretically and by mMn,~ of numerical experlnaents, with the leapfrog/Du Fort-F~rankpl (1,2,1) explicit method, the only three-level method currently employed to solve this equation. The former are generally found to be more accurate than the latter. ~? = (a)" exp i \ Nx ) ' i = v~, (8)