Comparisons of Quadrature Schemes with Arithmetic Mean Iterative Method for Second Kind Linear Fredholm Integral Equations
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Authors
Mohana Sundaram Muthuvalu
- School of Science and Technology, Universiti Malaysia Sabah, Locked Bag 2073, 88999 Kota Kinabalu, Sabah, Malaysia
Jumat Sulaiman
- School of Science and Technology, Universiti Malaysia Sabah, Locked Bag 2073, 88999 Kota Kinabalu, Sabah, Malaysia
Abstract
In this paper, we investigate the applications of two different quadrature schemes that is repeated trapezoidal (RT) and repeated modified trapezoidal (RMT) schemes via Arithmetic Mean iterative method to solve second kind linear Fredholm integral equations. Furthermore, the derivation and implementation of the proposed method are also included. Numerical tests and comparisons are given to illustrate the effectiveness of the proposed method.
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ISRP Style
Mohana Sundaram Muthuvalu, Jumat Sulaiman, Comparisons of Quadrature Schemes with Arithmetic Mean Iterative Method for Second Kind Linear Fredholm Integral Equations, Journal of Mathematics and Computer Science, 1 (2010), no. 3, 174--186
AMA Style
Muthuvalu Mohana Sundaram, Sulaiman Jumat, Comparisons of Quadrature Schemes with Arithmetic Mean Iterative Method for Second Kind Linear Fredholm Integral Equations. J Math Comput SCI-JM. (2010); 1(3):174--186
Chicago/Turabian Style
Muthuvalu, Mohana Sundaram, Sulaiman, Jumat. "Comparisons of Quadrature Schemes with Arithmetic Mean Iterative Method for Second Kind Linear Fredholm Integral Equations." Journal of Mathematics and Computer Science, 1, no. 3 (2010): 174--186
Keywords
- Linear Fredholm equations
- repeated trapezoidal
- repeated modified trapezoidal
- Arithmetic Mean
MSC
- 41A55
- 45A05
- 45B05
- 65D32
- 65F10
References
-
[1]
A. R. Abdullah, The four point Explicit Decoupled Group (EDG) method: A fast Poisson solver, Int. J. Comput. Math., 38 (1991), 61--70
-
[2]
T. Allahviranloo, E. Ahmady, N. Ahmady, K. S. Alketaby , Block Jacobi two-stage method with Gauss-Sidel inner iterations for fuzzy system of linear equations, Appl. Math. Comput., 175 (2006), 1217--1228
-
[3]
K. E. Atkinson , The Numerical Solution of Integral Equations of the Second Kind, Cambridge University Press, Cambridge (1997)
-
[4]
C. T. H. Baker, The Numerical Treatment of Integral Equations, Clarendon Press, Oxford (1977)
-
[5]
Z. Chen, C. A. Micchelli, Y. Xu, Fast collocation methods for second kind integral equations, SIAM J. Numer. Anal., 40 (2002), 344--375
-
[6]
Z. Chen, B. Wu, Y. Xu, Fast numerical collocation solutions of integral equations, Commun. Pure Appl. Anal., 6 (2007), 643--666
-
[7]
D. J. Evans, M. S. Sahimi , The Alternating Group Explicit iterative method (AGE) to solve parabolic and hyperbolic partial differential equations, Ann. Rev. Num. Fluid Mech. Heat Trans., 2 (1988), 283--389
-
[8]
H. Kaneko, A projection method for solving Fredholm integral equations of the second kind, Appl. Numer. Math., 5 (1989), 333--344
-
[9]
D. P. Laurie, Computation of Gauss-type quadrature formulas, J. Comput. Appl. Math., 127 (2001), 201--217
-
[10]
F.-R. Lin, Preconditioned iterative methods for the numerical solution of Fredholm equations of the second kind, Calcolo, 40 (2003), 231--248
-
[11]
K. Maleknejad, M. T. Kajani , Solving second kind integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions, Appl. Math. Comput., 145 (2003), 623--629
-
[12]
M. S. Muthuvalu, J. Sulaiman , Half-Sweep Geometric Mean method for solution of linear Fredholm equations, Matematika, 24 (2008), 75--84
-
[13]
M. S. Muthuvalu, J. Sulaiman, Half-Sweep Arithmetic Mean method with high-order Newton-Cotes quadrature schemes to solve linear second kind Fredholm equations, Journal of Fundamental Sciences, 5 (2009), 7--16
-
[14]
S. O. Oladejo, T. A. Mojeed, K. A. Olurode, The application of cubic spline collocation to the solution of integral equations, J. Appl. Sci. Res., 4 (2008), 748--753
-
[15]
M. Othman, A. R. Abdullah, An efficient Four Point Modified Explicit Group Poisson solver, Int. J. Comput. Math., 76 (2000), 203--217
-
[16]
A. D. Polyanin, A. V. Manzhirov, Handbook of Integral Equations, CRC Press, Florida (1998)
-
[17]
V. Ruggiero, E. Galligani, An iterative method for large sparse systems on a vector computer, Comput. Math. Appl., 20 (1990), 25--28
-
[18]
J. Saberi-Nadjafi, M. Heidari, Solving linear integral equations of the second kind with repeated modified trapezoid quadrature method, Appl. Math. Comput., 189 (2007), 980--985
-
[19]
M. S. Sahimi, A. Ahmad, A. A. Bakar, The Iterative Alternating Decomposition Explicit (IADE) method to solve the heat conduction equation, Int. J. Comput. Math., 47 (1993), 219--229
-
[20]
M. S. Sahimi, M. Khatim, The Reduced Iterative Alternating Decomposition Explicit (RIADE) method for diffusion equation. Pertanika Journal of Science and Technology, Pertanika Journal of Science and Technolology, 9 (2001), 13--20
-
[21]
J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, Springer-Verlag, New York, (1993)
-
[22]
W. Wang, A new mechanical algorithm for solving the second kind of Fredholm integral equation, Appl. Math. Comput., 172 (2006), 946--962