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Nonlinear Mathematics for Uncertainty and its Applications pp 463–470Cite as

A New Numerical Method for Solving Convection-Diffusion Equations

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Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

Abstract

In this paper, we using semi-discrete method, transformed convection-diffusion equation into a ODEs: \(\frac{dU(t)}{dt}\) = AU(t), then we get the solution of the ODEs: U(t) = e tA U0. Furthermore, we give a numerical approximation for e tA and get a special difference scheme for solving the convection-diffusion equation which improve the accuracy order and stability condition greatly. The accuracy order is fourth order and second order in space and time direction respectively. Finally, numerical result shows that this method is effective.

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References

  1. Ismail, H.N.A., Elbarbary, E.M.E. Salem, G.S.E.: Restrictive Taylor’s approximation for solving convection-diffusion equation. Appl. Math. Comput. 147, 355-363 (2004)

    Google Scholar 

  2. Salkuyeh, D.K.: On the finite difference approximation to the convection-diffusion equation. Appl. Math. Comput. 179, 79–86 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  3. Smith, G.D.: Numerical Solution of Partial Differential Equations(finite difference method). Oxford University Press, Oxford (1990)

    Google Scholar 

  4. Sousa, E.: The controversial stability analysis. Appl. Math. Comput. 145, 777–794 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Thomas, J.W.: Numerical Partial Differential Equations(finite difference methods). Springer, New York (1995)

    MATH  Google Scholar 

  6. Varga, R.S.: Matrix Iterative Analysis. Springer, Berlin (2000)

    Book  MATH  Google Scholar 

  7. Zhang, W.S.: Finite Difference Methods for Partial Differential Equation in Science Computation. Higher Education Press, Beijing (2006)

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Mathematics and statistics, Tianshui Normal University, Tianshui, 741000, P.R. China

    Hengfei Ding & Yuxin Zhang

Authors
  1. Hengfei Ding
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  2. Yuxin Zhang
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Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

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© 2011 Springer-Verlag Berlin Heidelberg

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Ding, H., Zhang, Y. (2011). A New Numerical Method for Solving Convection-Diffusion Equations. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_56

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  • DOI: https://doi.org/10.1007/978-3-642-22833-9_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

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