Proyecciones Journal of Mathematics Vol. 31, N^o 1, pp. 65-79, March 2012. Universidad Católica del Norte Antofagasta - Chile

 

Half-Sweep Geometric Mean Iterative Method for the Repeated Simpson Solution of Second Kind Linear Fredholm Integral Equations

 

Mohana Sundaram Muthuvalu

University Malaysia Sabah, Malaysia

Jumat Sulaiman

University Malaysia Sabah, Malaysia

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ABSTRACT

In previous studies, the effectiveness of the Half-Sweep Geometric Mean (HSGM) iterative method has been shown in solving first and second kind linear Fredholm integral equations using repeated trapezoidal (RT) discretization scheme. In this work, we investigate the efficiency of the HSGM method to solve dense linear system generated from the discretization of the second kind linear Fredholm integral equations by using repeated Simpson's ^ (RS1) scheme. The formulation and implementation ofthe proposed method are also presented. In addition, several numerical simulations and computational complexity analysis were also included to verify the efficiency of the proposed method.

Keywords: Linear Fredholm equations, half-sweep iteration, repeated Simpson, Geometric Mean

Mathematics Subject Classification: 41A55, 45A05, 45B05, 65F10, 65Y20

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Mohana Sundaram Muthuvalu

School of Science and Technology, Universiti Malaysia Sabah

Jalan UMS, 88400 Kota Kinabalu,

Sabah, Malaysia

e-mail : sundaram_at2@yahoo.com

and

Half-Sweep Geometric Mean Iterative Methodfor the ... 79

Jumat Sulaiman

School of Science and Technology,

Universiti Malaysia Sabah

Jalan UMS, 88400 Kota Kinabalu,

Sabah,

Malaysia

e-mail : jumat@ums.edu.my

Received : August 2010. Accepted : September 2011