Numerical Solution of Poly-Harmonic Equations

A. G. Terentiev

Computer Science and Information Technologies, Computer Science and Information Technologies 2007

A. G. Terentiev

Last modified: 2021-01-06

Abstract

A poly-harmonic equation of any order in a two-and three-dimensional space is considered. In the beginning Green's integral identity for poly-harmonic functions is reduced to a set of integral equations in which integration is carried out only on the boundary of a domain. Then the boundary element method (BEM) is applied to a numerical solution of obtained integral equations. The numerical example testifies to high accuracy of the method.

Keywords

Numerical Solution; Poly-Harmonic Equations; three-dimensional space

References

1. Terentiey A.G, “Numerical Solution of Biharmonic Equation”. In: Proc. of 5th International Workshop on Computer Science and Information Technologies (CSIT’2003), Vol. 2. USATU, Ufa, Russia, 2003,pp.261-263

2. Vekua IN, “New elliptic equations methods”, FML, Moscow, 1948.

3. Brebbia C.A., Telles J.C.F., Wrobel L.C., Boundary "Element Techniqoues". Springer-Verlag, Berlin, 1984.

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