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| Combined super compact finite difference scheme and application to simulation of shallow water equations |
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| DOI：10.7511/jslx20086148 |
| KeyWord:Combined super compact finite difference scheme(CSCD),Adams-Bashforth scheme,Resolution |
| LIN Dong1 2 ZHAN Jie-min1 3 |
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| Abstract: |
| A combined super compact finite difference scheme(CSCD) is proposed.Numerical characteristics of CSCD is analysed and compared with other symmetric difference schemes.The truncation error of CSCD is derived and compared with some symmetric finite difference methods having the same order of accuracy,which shows that CSCD has the smallest coefficients in error terms.By using Fourier analysis on the capability of resolution,we conclude that CSCD gives higher resolution,with respect to other symmetric finite difference methods.Tenth-order CSCD is applied to numerical simulation of KdV-Burgers equation and shallow water equations.Two tests are given.Numerical experiment point out that CSCD has properties of not only higher accuracy but also good stability and convergence. |