Wavelet application in solving ordinary differential equations using Galerkin method

Jasmina Veta Buralieva; Sanja Kostadinova; Katerina Hadzi-Velkova Saneva

Jasmina Veta Buralieva Faculty of computer science, University “Goce Delcev”-Stip
Sanja Kostadinova Faculty of Electrical Engineering and Information Technologies, Skopje;
Katerina Hadzi-Velkova Saneva Faculty of Electrical Engineering and Information Technologies, Skopje;

Abstract

The Galerkin method is one of the most used methods for finding numerical solutions of ordinary and partial differential equations. Its simplicity makes it suitable for many applications. In this paper we show that the wavelet-Galerkin method is an improvement over the standard Galerkin method for ordinary differential equations.

References

A. H. Siddiqi. (2004). Applied Functional Analysis: Numerical Methods, Wavelet Methods and Image Processing. New York: Markel Dekker.

C. Qian, J. Weiss (1993). Wavelets and numerical solution of partial deifferential equations. Journal of Computational Physics, Vol.106, Issue 1, pp.155-175.

C. S. Salimath, Wavelets in Numerical Analysis of Differential and Integral Equations. Karnatak University Dharwad: Research Scholar Department of Mathematics.

I. Daubechies, (1992). Ten lecture of Wavelets. Philadelphia: SIAM.

G. G. Walter, X. Shen, (2000). Wavelets and Other Orthonormal System With Application. SRC Press, Secound Edition.

M. W. Frazier, (1999). An Introduction to Wavelets Through Linear Algebra. New York: Springer-Verlag.

R. T. Ogden, (1997). Essential wavelets for Statistical Applications and Data Analysis. Boston: Birkhauser.

S. G. Mallat, (1989). Multiresolution approximations and wavelet orthonormal basis of , Trans. Amer. Math. Soc., 315, pp. 69-87.

S. Kostadinova, J. Veta Buralieva, K. Hadzi-Velkova Saneva, (2013). Wavelet-Galerkin solution of some ordinary differential equations, Proceedings of the XI International Conference ETAI 2013, 26-28 September 2013, Ohrid, Macedonia.

S. Mallat, (1989). Multiresolution approximation and wavelets. Trans. Amer. Math. Soc., 315, pp. 69-8

T. Lofti, K. Mahdiani. (2007). Numerical solution of baundary value problem by using wavelet-Galerkin methods. Mathematical Sciences, Vol. 1, No. 3, pp.7-18.

U. Lepik, (2007). Application of Haar wavelet transform to solving integral and differential equations. Proc. Estonian Acad. Sci. Phys. Math., Vol.56, no.1, pp. 28-46.

Vinod Mishra, Sabina, Wavelet Galerkin Solutions of ordinary differential equations. Int. Journal of Math. Analysis, Vol. 5, 201, no. 9, 408-424.