Iterative Method for the Solution of Fredholm Integral Equations of the 2nd kinds via Matrices
|Published in:||Issue 1, (Vol. 15) / 2021|
|Author(s):||AHMED Hela Shawkat, MOHAMMED Sizar Abid|
|Abstract.||It was given a matrix iterative algorithm to solve the approximate equations Fredholm integral of the second kind. Modify the algorithm ideas of iterated kernels through a matrix of Hilbert. Thus, some numerical examples are observed results while reducing solution, given the procedure to replace the kernel technology given to the equation almost an integrated nucleus of a degraded kernel in a matrix form, and then to create a repeating sequence of iterative solutions.|
|Keywords:||Integral Equations, Iterative Methods, Approximate Solutions. Matrix Treatment|
1. Andrei D. polyanin and alexander V. Manzhirov, Handbook of Integral Equations, CRC press, 2008.
2. Burden Richard L. and Faires J. Doudlas, Numerical Analysis, PWS publishing company, company, Boston? 2010.
3. Baker C.T.H , the numirecal Treatment of Integral Equations, Clarendom press, Oxford, 4th edition? 1977
4. Guangqing L. and Gnaneshwar N., Iteration methods for fredholm integral equations of the second kind, Computes and Mathematics with Applications, Vol. 53(2007) 886-894.
5. Grahan I.G and S. Joe and I.H. Sloan, Iterated Galerkin versus iterated collocation for integral equations of second kind, IMA J. Numer . Anal, 5 (1985)355-369.
6. Atkinson K.E., The numerical Solution of Integral equation of the second kind, cambridge University pree, Cambridge, 1977.
7. De Bonnis M. C . and Laurita C ., Numerical Treatment of second kind fredholm integral equation systems on Bounded Intervals , Journal of Computation and Applied Mathematics, (2008) 64-87.
8. Kaneko H. and Xn Y., Super convergence of the iterated Galerkin methods for Hammerstein equations, SIAM J. Numer. Anal., Vol 33 (1996) 1048-1064.
9. Shoukralla, E.S, An algorithm For The Solution Of a certain Singular Integral Equation Of The First Kind, Intern. J. Compute Math., Vol 69 (1998) 165-173.
10. Shoukralla, E. S, Approximate Solution to weakly singular integral equations J. Apple. Math. Modeling, Vol 20 (1996) 800-803.
11. Verlane A.F. and Cazakov V. C., Integral Equations, Nauka Domka, Kiev, USSR,1986.
12. Chen Z., Micchelli C.A and Xu Y., Fast collection methods for second kind integral equations, SIAM J. Numer. Anal., Vol 40 (2002) 344-375.
13. Richard L. Burden and J. Douglas Faires, "Numerical Analysis", Library of Congress, 2011
14. J. Rashidinia ∗, M. Zarebnia, "Convergence of approximate solution of system of Fredholm integral equations", J. Math. Anal. Appl. 333 (2007) 1216–1227.
15. H. Kaneko, Y. Xu, "Super convergence of the iterated Galerkin methods for Hammerstein equations", SIAM J. Numer. Anal., 33 (1996), pp. 1048–1064.
16. Guangqing Longa,b,_, Gnaneshwar Nelakantib,c, "Iteration methods for Fredholm integral equations of the second kind", Computers and Mathematics with Applications 53 (2007) 886–894.
17. 17 Graham I.G., S. Joe, I.H. Sloan, "Iterated Galerkin versus iterated collocation for integral equations of second kind", IMA J.Numer. Anal., 5 (1985), pp. 355–369
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