Heuristic Method for Judging the Computational Stability of the Difference Schemes of the Biharmonic Equation

In this paper, we research the standard 13-point difference schemes for solving the biharmonic equation. Heuristic method is applied to judging the stability of multi-level difference schemes of the biharmonic equation. It is showed that the standard 13-point difference schemes are stable.

• Guang Zeng
• Jin Huang
• Zicai Li

• Finite-difference equation
• computational stability
• hirt method.

[1] Courant R. and Hilbert D., Methods of Mathematical Physics, Vol. I.
Wiley-Interscience Publishers, New York, 1953.
[2] Lu T., Zhou G.F and Lin Q., High order difference methods for the
biharmonic equation, Acta Math. Sci., Vol. 6, pp. 223-230, 1986.
[3] Quarteroni A. and Valli A., Numerical approximation of Partial Differential
Equations, Springer-Verlag, Berlin, 1994.
[4] Stys T., A higher accuracy finite difference method for an elliptic equation
of order four, J. Computational and Applied Mathematics, Vol. 164-165,
pp. 661-672, 2004.
[5] Hirt C. W., Heuristic stability theory for finite-difference equations, J.
Comp. Phys., 1968, 2: 339.
[6] Lin W. T., Ji Z. Z. and Wang B., A comparative analysis of computational
stability for linear and non-linear evolution equations. Advances in
Atmospheric Sciences, 2002, 19(4): 699-704.
[7] Samarskii A. A., The theory of Difference Schemes, New York: Marcel
Dekker, 2001.
[8] Thomas J. W., Numerical Partial Differential Equations Finite Difference
Methods, New York: Springer-Verlag, 1997.