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Half-Sweep Geometric Mean Method for Solution of Linear Fredholm Equations

Muthuvalu M.S., and Sulaiman J., (2008) Half-Sweep Geometric Mean Method for Solution of Linear Fredholm Equations. Matematika, 24 (1). pp. 75-84. ISSN 01278274

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Official URL: http://www.fs.utm.my/matematika/images/stories/matematika/20082418.pdf

Affiliations

Universiti Malaysia Sabah, School of Science and Technology
Universiti Malaysia Sabah, School of Science and Technology

Abstract

The objective of this paper is to examine the application of the Half-Sweep Geometric Mean (HSGM) method by using the half-sweep approximation equation based on quadrature formula to solve linear integral equations of Fredholm type. The formulation and implementation of the Full-Sweep Geometric Mean (FSGM) and Half-Sweep Geometric Mean (HSGM) methods are also presented. Some numerical tests were carried out to show that the HSGM method is superior to the FSGM method in the sense of complexity and execution time.

Item Type:Journal
Keywords:Fredholm integral equations; quadrature formula; half-sweep geometric mean method
Subjects:Q Science, Computer Science
ID Code:5462

[1] M.A. Abdou, Fredholm-Volterra integral equation with singular kernel, Applied Mathematics and Computation 137 (2003), 231-243.

[2] A.R. Abdullah, The four point Explicit Decoupled Group (EDG) method: A fast Poisson solver, International Journal Computer Mathematics 38 (1991), 61-70.

[3] 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, Applied Mathematics and Computation 175 (2006),1217-1228.

[4] S.A. Ashour, Numerical solution of integral equations with finite part integrals, Internat. J. Math. & Math. Sci. 22 (1) (1999), 155-160.

[5] C.T.H. Baker, The Numerical Treatment of Integral Equations, Clarendon Press Oxford, 1977.

[6] H.J. Dobner, Kernel-Splitting Technique for Enclosing the Solution of Fredholm Equations of the First Kind, Reliable Computing 8 (2002), 469-479.

[7] D.J. Evans & M.S. Sahimi, The Alternating Group Explicit iterative method (AGE) to solve parabolic and hyperbolic partial di®erential equations, Ann. Rev. Num. Fluid Mech. And Heat Trans. 2 (1988), 283-389.

[8] A. Frommer & D.B. Szyld, Asynchronous two-stage iterative methods, Numerische Mathematik 69 (1994), 141-153.

[9] A. Ibrahim & A.R. Abdullah, Solving the two-dimensional di®usion equation by the four point Explicit Decoupled Group (EDG) iterative method, International Journal Computer Mathematics 58 (1995), 253-256.

[10] D.P. Laurie, Computation of Gauss-type quadrature formulas, Journal of Computational and Applied Mathematics 127 (2001), 201-217.

[11] K. Maleknejad, R. Mollapourasl & K. Nouri, Convergence of numerical solution of the Fredholm integral equation of the ¯rst kind with degenerate kernel, Applied Mathematics and Computation 181 (2006), 1000-1007.

[12] A.D. Polyanin & A.V. Manzhirov, Handbook of integral equations, CRC Press LCC, 1998.

[13] M.T. Rashed, An expansion method to treat integral equations, Applied Mathematics and Computation 135 (2003), 65-72.

[14] V. Ruggiero & E. Galligani, An iterative method for large sparse systems on a vector computer, Computer Math. Applic. 20 (1990), 25-28.

[15] M.S. Sahimi, A. Ahmad & A.A. Bakar, The Iterative Alternating Decomposition Explicit (IADE) method to solve the heat conduction equation, International Journal of Computer Mathematics 47 (1993), 219-229.

[16] M.S. Sahimi & M. Khatim, The Reduced Iterative Alternating Decomposition Explicit (RIADE) method for diffusion equation, Pertanika J. Sci. And Technol. 9(1) (2001), 13-20.

[17] J. Sulaiman & A.R. Abdullah, Beberapa kaedah lelaran kumpulan tak tersirat nyah-pasangan dengan separuh sapuan multigrid bagi persamaan Poisson, Sains Malaysiana 28 (1999), 161-172.

[18] J. Sulaiman, M.K. Hasan & M. Othman, The Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) method for diffusion equations, In. J. Zhang, J.-H. He and Y. Fu (Eds). Computational and Information Science 2004. Lecture Note on Computer Science (LNCS 3314) (2004), 57-63.

[19] J. Sulaiman, M. Othman & M.K. Hasan, Quarter-Sweep Iterative Alternating Decomposition Explicit algorithm applied to diffusion equations, International Journal of Computer Mathematics 81(12) (2004), 1559-1565.

[20] J. Sulaiman, M. Othman & M.K. Hasan, A new Half-Sweep Arithmetic Mean (HSAM) algorithm for two-point boundary value problems, Proceedings of the International Conference on Statistics and Mathematics and Its Application in the Development of Science and Technology, Bandung, Indonesia (2004), 169-173.

[21] J. Sulaiman, M. Othman & M.K. Hasan, Half-Sweep Arithmetic Mean method using finite element approximation for Poisson's equation, Conference on Applied Mathematics, Bandung Institute of Technology, Indonesia (2005).

[22] J. Sulaiman, M. Othman & M.K. Hasan, A fourth-order finite difference solver for Poisson's equations via the Half-Sweep Arithmetic Mean (HSAM) method, Proceedings of the First IMT-GT Regional Conference on Mathematics, Statistics and Their Applications, Parapat, Indonesia (2005), 139-146.

[23] J. Sulaiman, M. Othman, N. Yaacob & M.K. Hasan, A new Half-Sweep Geometric Mean (HSGM) algorithm for two-point boundary value problems, Submitted to Sains Malaysiana (2006).

[24] J. Sulaiman, M. Othman, N. Yaacob & M.K. Hasan, Half-Sweep Geometric Mean (HSGM) method using fourth- order finite difference scheme for two-point boundary problems, Proceedings of the First International Conference on Mathematics and Statistics (ICOMS-1), Bandung, Indonesia (2006). (In CD-Form)

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