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| High-order compact scheme and its stability analysis for the pollutant diffusion equation |
| Received:August 26, 2005 Revised:June 09, 2006 |
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| DOI：10.7511/jslx20076154 |
| KeyWord:pollutant diffusion,diffusion equation,finite difference,stable schemes,explicit scheme,compact scheme |
| LIN Jian-guo XIE Zhi-hua ZHOU Jun-tao |
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| Abstract: |
| An explicit numerical method which has arbitrary order of accuracy in time was derived in this paper,including the analysis of the stability and the accuracy of the pollutant diffusion equation.The conventional explicit Forward Time Central Space scheme(FTCS) is the specific form with first order accuracy of the proposed method.The theoretical analysis demonstrated that the stable region would expand along with the increase of the order of accuracy and the proposed explicit method was unconditionally stable when remaining the infinite order of accuracy.Finally,the validity of the proposed method was tested by a numerical example and it is shown that the numerical results agree quite well with the anterior theoretical analysis.And it also reveals the relationship between the stability and the accuracy,and provides the advisory principle for the development of the high-performance computational schemes. |
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