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High Order Locally One-Dimensional Method for Parabolic Problems

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Computational and Information Science (CIS 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3314))

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Abstract

We propose a high order locally one-dimensional scheme for solving parabolic problems. The method is fourth-order in space and second-order in time. It is unconditionally stable and provides a computationally efficient implicit scheme. Numerical experiments are conducted to test its high accuracy and to compare it with other schemes.

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References

  1. Ciment, M., Leventhal, S.H.: Higher order compact implicit schemes for the wave equation. Math. Comp. 29, 985–994 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  2. Douglas, J., Peaceman, D.W.: Numerical solution of two-dimensional heat flow problems. American Institute of Chemical Engineering Journal 1, 505–512 (1959)

    Google Scholar 

  3. Douglas, J.: On the numerical integration of \(\frac{\partial^{2}u}{{\partial}x^{2}}\) + \(\frac{\partial^{2}u}{{\partial}y^{2}}\) = \(\frac{{\partial}u}{{\partial}t}\) by implicit methods. J. Soc. Ind. Appl. Math. 3, 42–65 (1959)

    Google Scholar 

  4. D’yakonov, E.: Difference schemes with splitting operators for multidimensional unsteady problems (English translation). URSS Comp. Math. 3, 581–607 (1963)

    Google Scholar 

  5. Kalita, J.C., Dalal, D.C., Dass, A.K.: A class of higher order compact schemes for the unsteady two-dimensional convection-diffusion equation with variable convection coefficients. Int. J. Numer. Methods Fluids 38, 1111–1131 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Karaa, S., Zhang, J.: High order ADI method for solving unsteady convectiondiffusion problems. J. Comput. Phys. 198, 1–9 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. McKee, S.: High accuracy ADI methods for hyperbolic equations with variable coefficients. J. Inst. Maths. Applics. 11, 105–109 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  8. Mitchell, A.R., Fairweather, G.: Improved forms of the alternating direction methods of Douglas, Peaceman, and Rachford for solving parabolic elliptic equations. Numer. Math. 6, 285–292 (1964)

    Article  MATH  MathSciNet  Google Scholar 

  9. Noye, B.J., Tan, H.H.: Finite difference methods for solving the two-dimensional advection-diffusion equation. Int. J. Numer. Methods Fluids 26, 1615–1629 (1989)

    MathSciNet  Google Scholar 

  10. Peaceman, D.W., Rachford Jr., H.H.: The numerical solution of parabolic and elliptic differential equations. J. Soc. Ind. Appl. Math. 3, 28–41 (1959)

    MathSciNet  Google Scholar 

  11. Strikwerda, J.C.: Difference Schemes and Partial Differential Equations. Wadsworth & Brooks/Cole, Pacific Grove (1989)

    MATH  Google Scholar 

  12. Spotz, W.F.: High-Order Compact Finite Difference Schemes for Computational Mechanics. Ph.D. Thesis, University of Texas at Austin, Austin, TX (1995)

    Google Scholar 

  13. Yanenko, N.: Convergence of the method of splitting for the heat conduction equations with variable coefficients (English tradition). USSR Comp. Math. 3, 1094–1100 (1963)

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Sultan Qaboos University, P. O. Box 36, Al-khod 123, Muscat, Sultanate of Oman

    Samir Karaa

Authors
  1. Samir Karaa
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Editor information

Editors and Affiliations

  1. School of Electronic Science and Technology, Anhui University, Hefei, Anhui, China

    Jun Zhang

  2. College of Science, Donghua University, 1882 Yan’an Xilu Road, 20051, Shanghai, China

    Ji-Huan He

  3. BASICS, Department of Computer Science and Engineering, Shanghai Jiao Tong University, 200030, Shanghai, China

    Yuxi Fu

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© 2004 Springer-Verlag Berlin Heidelberg

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Karaa, S. (2004). High Order Locally One-Dimensional Method for Parabolic Problems. In: Zhang, J., He, JH., Fu, Y. (eds) Computational and Information Science. CIS 2004. Lecture Notes in Computer Science, vol 3314. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30497-5_20

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  • DOI: https://doi.org/10.1007/978-3-540-30497-5_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24127-0

  • Online ISBN: 978-3-540-30497-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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