Numerical Solution of Second Kind Linear Fredholm Integral Equations Using QSGS Iterative Method with High-Order Newton-Cotes Quadrature Schemes

The main purpose of this paper is to examine the effectiveness of the Quarter-Sweep Gauss-Seidel (QSGS) method in solving the dense linear systems generated from the discretization of the linear Fredholm integral equations of the second kind. In addition, the applications of the various orders of closed Newton-Cotes quadrature discretization schemes will be investigated in order to form linear systems. Furthermore, the basic formulation and implementation of the proposed method are also presented. The numerical results of test examples are also included in order to verify the performance of the proposed method.

[1]  Jumat Sulaiman,et al.  Half-Sweep Arithmetic Mean method with composite trapezoidal scheme for solving linear Fredholm integral equations , 2011, Appl. Math. Comput..

[2]  M. Othman,et al.  Implementation of Red Black Strategy to Quarter Sweep iteration for solving first order hyperbolic equations , 2008, 2008 International Symposium on Information Technology.

[3]  Jumat Sulaiman,et al.  A Parallel Halfsweep Multigrid Algorithm on the Shared Memory Multiprocessors , 2000 .

[4]  Khosrow Maleknejad,et al.  Solving second kind integral equations by Galerkin methods with hybrid Legendre and Block-Pulse functions , 2003, Appl. Math. Comput..

[5]  Mohamed Othman,et al.  Parallel Solution of High Speed Low Order FDTD on 2D Free Space Wave Propagation , 2007, ICCSA.

[6]  M.K. Hasan,et al.  The HSLO(3)-FDTD with direct-domain and temporary-domain approaches on infinite space wave propagation , 2005, 2005 13th IEEE International Conference on Networks Jointly held with the 2005 IEEE 7th Malaysia International Conf on Communic.

[7]  A. Saudi,et al.  Quarter-Sweep Arithmetic Mean Algorithm for water quality model , 2008, 2008 International Symposium on Information Technology.

[8]  Bin Wu,et al.  Fast numerical collocation solutions of integral equations , 2007 .

[9]  M. Othman,et al.  Half-Sweep Algebraic Multigrid (HSAMG) Method Applied to Diffusion Equations , 2006, HPSC.

[10]  Abdul Rahman Abdullah,et al.  A Comparative Study of Parallel Strategies for the Solution of Elliptic Pde's , 1996, Parallel Algorithms Appl..

[11]  K. Atkinson.  The Numerical Solution of Integral Equations of the Second Kind , 1997 .

[12]  David J. Evans,et al.  Explicit De-coupled Group Iterative Methods and their Parallel Implementations , 1995, Parallel Algorithms Appl..

[13]  J. Sulaiman,et al.  Numerical solutions of second kind Fredholm integral equations using Half-Sweep Geometric Mean method , 2008, 2008 International Symposium on Information Technology.

[14]  Abdul Rahman Abdullah.  The four point explicit decoupled group (EDG) Method: a fast poisson solver , 1991, Int. J. Comput. Math..

[15]  M Tavassolikajani.  Solving second kind integral equations with Hybrid Chebyshev and Block-Pulse functions , 2004 .

[16]  Weiming Wang.  A new mechanical algorithm for solving the second kind of Fredholm integral equation , 2006, Appl. Math. Comput..

[17]  S. O. Oladejo.  The Application of Cubic Spline Collocation to the Solution of Integral Equations , 2008 .

[18]  Dirk Laurie,et al.  Computation of Gauss-type quadrature formulas , 2001 .

[19]  Jumat Sulaiman,et al.  Half-Sweep Geometric Mean Method for Solution of Linear Fredholm Equations , 2008 .

[20]  Abdollah Hadi-Vencheh,et al.  Solving second kind integral equations with hybrid Fourier and block-pulse functions , 2005, Appl. Math. Comput..

[21]  Mohamed Othman,et al.  The Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) Method for Diffusion Equation , 2004, CIS.

[22]  Mohamed Othman,et al.  Red-Black Half-Sweep Iterative Method Using Triangle Finite Element Approximation for 2D Poisson Equations , 2007, International Conference on Computational Science.

[23]  Mohamed Othman,et al.  Implementation of the Parallel Four Points Modified Explicit Group Iterative Algorithm on Shared Memory Parallel Computer , 2001, PaCT.

[24]  F.-R. Lin.  Preconditioned iterative methods for the numerical solution of Fredholm equations of the second kind , 2003 .

[25]  Guangqing Long,et al.  Iteration methods for Fredholm integral equations of the second kind , 2007, Comput. Math. Appl..

[26]  A projection method for solving Fredholm integral equations of the second kind , 1989 .

[27]  M. Othman,et al.  An efficient four points modified explicit group poisson solver , 2000, Int. J. Comput. Math..

[28]  Mohamed Othman,et al.  MEGSOR iterative method for the triangle element solution of 2D Poisson equations , 2010, ICCS.

[29]  Mohamed Othman,et al.  Quarter-sweep iterative alternating decomposition explicit algorithm applied to diffusion equations , 2004, Int. J. Comput. Math..

[30]  Duo Zhang,et al.  Solving second kind Fredholm integral equations by periodic wavelet Galerkin method , 2006, Appl. Math. Comput..

[31]  Yuesheng Xu,et al.  Fast Collocation Methods for Second Kind Integral Equations , 2002, SIAM J. Numer. Anal..