Solving second kind linear Fredholm integral equations via Quarter-Sweep SOR iterative method
DOI:
https://doi.org/10.11113/mjfas.v6n2.191Keywords:
Linear Fredholm equations, Quarter-sweep iteration, Quadrature, Successive Over-Relaxation,Abstract
In this paper, we consider the numerical solutions of linear Fredholm integral equations of the second kind. The Quarter-Sweep Successive Over-Relaxation (QSSOR) iterative method is applied to solve linear systems generated from discretization of the second kind linear Fredholm integral equations using quadrature method. In addition, the formulation and implementation of the proposed method to solve the problem are also presented. Numerical tests and comparisons with other existing methods are given to illustrate the effectiveness of the proposed method.
References
W. Wang, Appl. Math. Comput., 172 (2006) 946-962.
K.E. Atkinson, The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, United Kingdom, 1997.
M.S. Muthuvalu and J. Sulaiman, Journal of Fundamental Sciences, 5(1) (2009) 7-16.
C. Allouch, P. Sablonnière, D. Sbibih and M. Tahrichi, J. Comput. Appl. Math., 233 (2010) 2855-2866.
G. Mastroianni and G. Monegato, SIAM J. Numer. Anal., 41(5) (2004) 1870-1892.
S.-Y. Kang, I. Koltracht and G. Rawitscher, Math. Comput., 72(242) (2003) 729-756.
J. Saberi-Nadjafi and M. Heidari, Appl. Math. Comput., 189 (2007) 980-985.
F.-R. Lin, Calcolo, 40 (2003) 231-248.
Y. Liu, Math. Comput. Model., 50 (2009) 465-469.
P. M. Prenter, SIAM J. Numer. Anal., 10 (4) (1973) 570-581.
K. Atkinson, I. Graham and I. Sloan, SIAM J. Numer. Anal., 20 (1) (1983) 172-186.
Z. Chen, B. Wu and Y. Xu, Commun. Pure Appl. Anal., 6(3) (2007) 643-666.
C. Cattani and A. Kudreyko, Appl. Math. Comput., 215 (2010) 4164-4171.
G. Long, M.M. Sahani and G. Nelakanti, Appl. Math. Comput., 215 (2009) 147-155.
J.-Y. Xiao, L.-H. Wen and D. Zhang, Appl. Math. Comput., 175 (2006) 508-518.
A.R. Abdullah, Int. J. Comput. Math., 38 (1991) 61-70.
M.S. Muthuvalu and J. Sulaiman, Matematika, 24(1) (2008) 75-84.
M. Othman, J. Sulaiman and A.R. Abdullah, Malaysian Journal of Computer Science, 13(2) (2000) 1-6.
J. Sulaiman, M.K. Hasan and M. Othman, Lect. Notes Comput. Sc., LNCS 4487 (2007) 326-333.
A.R. Abdullah and N.H.M. Ali, Parallel Algorithms and Applications, 10 (1996) 93-103.
W.S. Yousif and D.J. Evans, Parallel Algorithms and Applications, 7 (1995) 53-71.
M. Othman and A.R. Abdullah, Int. J. Comput. Math., 76 (2000) 203-217.
S.I. Rakhimov and M. Othman, Sains Malaysiana, 38(5) (2009) 729-733.
J. Sulaiman, M. Othman and M.K. Hasan, Chamchuri J. Math., 1(2) (2009) 93-103
M. Othman and A.R. Abdullah, Lect. Notes Comput. Sc., LNCS 2127 (2001) 480-489.
J. Sulaiman, M. Othman and M.K. Hasan, Int. J. Comput. Math., 81(12) (2004) 1559-1565.
N. Jha and B.K. Mishra, International Journal of Mathematical Modeling, Simulation and Applications, 1(1) (2008) 41-45.
S. Yang and M.K. Gobbert, Appl. Math. Lett., 22 (2009) 325-331.
N.H.M. Ali and L.S. Chong, Appl. Math. Comput., 191 (2007) 533-542.
S.I. Rakhimov and M. Othman, Sains Malaysiana, 38(5) (2009) 729-733.
A.D. Polyanin and A.V. Manzhirov, Handbook of Integral Equations, CRC Press LCC, Florida, 1998.
S. Rahbar and E. Hashemizadeh, Proceedings of the World Congress on Engineering, 2 (2008) 933-937.
