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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1329629Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1041
 Courant R. and Hilbert D., Methods of Mathematical Physics, Vol. I. Wiley-Interscience Publishers, New York, 1953.
 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.
 Quarteroni A. and Valli A., Numerical approximation of Partial Differential Equations, Springer-Verlag, Berlin, 1994.
 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.
 Hirt C. W., Heuristic stability theory for finite-difference equations, J. Comp. Phys., 1968, 2: 339.
 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.
 Samarskii A. A., The theory of Difference Schemes, New York: Marcel Dekker, 2001.
 Thomas J. W., Numerical Partial Differential Equations Finite Difference Methods, New York: Springer-Verlag, 1997.