IJPAM: Volume 107, No. 1 (2016)

AN APPROXIMATE SOLUTION OF FREDHOLM INTEGRAL
EQUATION OF THE SECOND KIND BY BAND-LIMITED
SCALING FUNCTION

Gopal Priyadarshi$^1$, B.V. Rathish Kumar$^2$
$^1$Department of Mathematics & Statistics
Indian Institute of Technology Kanpur
Kanpur, 208016, INDIA


Abstract. Fredholm integral equation of the second kind appears naturally in different areas of mathematics, physics and engineering. In this paper we consider Fredholm integral equation of the second kind with convolution type kernel. We assume $f$ in the approximation space and prove the existence and uniqueness of approximate solution by band-limited scaling function. Since these functions are infinitely differentiable and possess decay property, methods based on these functions would be very accurate. Convergence analysis has been discussed to validate our approximate solution.

Received: January 16, 2016

AMS Subject Classification: 41B05, 45L05, 65G99

Key Words and Phrases: scaling function, orthonormal wavelet, band-limited wavelet, approximation space, Fredholm integral equation of the second kind, convolution

Download paper from here.




DOI: 10.12732/ijpam.v107i1.3 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 1
Pages: 23 - 34


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).