An Iterative Solution for Second Order Linear Fredholm Integro-Differential Equations
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The objective of this paper is to analyze the application of the quarter-sweep iterative concept on Quadrature-Difference schemes namely central difference (CD)-composite trapezoidal (CT) with the Gauss-Seidel iterative method to solve second order linear Fredholm integro-differential equations. The formulation and implementation of the Full-, Half- and Quarter-Sweep Gauss-Seidel methods namely FSGS, HSGS and QSGS are presented for performance comparison. Furthermore, computational complexity and percentage reduction calculations are also presented with several numerical simulations. The numerical results show that the proposed QSGS method with the corresponding discretization schemes is superior compared to the FSGS and HSGS methods.
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Aruchunan, E.; Khajohnsaksumeth, N.; Wiwatanapataphee, Benchawan (2016)© 2016 IEEE.The Fredholm Integro-differential equations (IDEs) of the second kind appear in many scientific applications. Mathematical methods for the solution of the Fredholm IDEs have been developed over the last decade. ...
Xu, X.; Pan, H.; Wei, W.; Wang, G.; Liu, Wan-Quan (2018)© Springer Nature Singapore Pte Ltd. 2018. When the first order variational models are used for multiplicative noise removal, there always some staircase effect, contract reduction, and corner smearing. In this paper, we ...
Akhir, K.; Othman, M.A.; Suleiman, M.; Majid, Z.; Sulaiman, J.; Muthuvalu, M.; Aruchunan, Elayaraja (2014)In this paper, we consider the numerical solutions of homogeneous Helmholtz equations of the second order. The Quarter-Sweep Modified Successive Over-Relaxation (QSMSOR) iterative method is applied to solve linear systems ...