Legendre wavelet method for solving Hammerstein integral equations of the second kind

Subject Areas : Applied Mathematics

Sh Javadi ¹ , J Saeidian ^{2 *} , F Safari ³

1 - Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani avenue, Tehran 15618-36314, Iran
2 - Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani avenue, Tehran 15618-36314, Iran
3 - Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani avenue, Tehran 15618-36314, Iran

Received: 2015-09-20 Accepted : 2015-09-20 Published : 2015-12-01

Keywords: Legendre wavelets, Fredholm-Hammerstein integral equations, Volterra-Hammerstein integral equations, Newton&#039, s method, Operational matrix,

Abstract :

An ecient method, based on the Legendre wavelets, is proposed to solve thesecond kind Fredholm and Volterra integral equations of Hammerstein type.The properties of Legendre wavelet family are utilized to reduce a nonlinearintegral equation to a system of nonlinear algebraic equations, which is easilyhandled with the well-known Newton's method. Examples assuring eciencyof the method and its superiority are presented.