An Approximate Solutions of two Dimension Linear Mixed Volterra- Fredholm Integral Equation of the Second Kind via Iterative Kernel Method
DOI:
https://doi.org/10.26750/paperKeywords:
Retia test, Iterative kernel method and MVFIE-2, methodAbstract
Abstract:
In this work, we reformulate and apply iterative kernel method (IKM) for solving two dimension mixed Volterra-Fredholm integral equation of the second kind (MVFIE-2). The suitable algorithm for IKM is suggested and the programming for of the algorithm of the technique is written by Matlab programs. The computer application for the algorithm is tested on a number numerical examples. The results which are obtained by this technique compared with exact solution and some new theorems are proved; for decision the results computing the least square error (LSE) of the IKM and running time (RT) for the program.
References
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Volterra-Fredholm integral equations of the second kind. Journal of Mathematica. 33(2), 191-206.
Tenwich, M. C. (2012). Error estimates for numerical solutions of one and two dimension Integral
equations, PhD Thesis, University of Leeds department of applied Mathematics.
Wazwaz, A.M. (2011). Linear and non-linear integral equations methods and applications. Springer-Verlag
Berlin Heidelberg.
Zhong C. Z. and Jiang W. (2012). An approximate solution for a mixed linear Volterra–Fredholm integral
Equation. Journal Applied Mathematics and letter, 25(1), 1131-1134.
LE MATEMATICHE. Vol. LX (I), 41-58.
Berdawood, K. A. (2015). Computational method for solving mixed Volterra Fredholm integral equation of
the second kind, MSc thesis Salahaddin University.
Ibrahim, H. Attah, F. and Gyegwe, T. (2016). On the solution of Volterra-Fredholm and mixed Volterra-
Fredholm integral equations using the new iterative method. Journal of applied Mathematics. 6(1), 1-5.
Hafez R. M., Doha E. H., Bhrawy A. H. and Baleanu D. (2017). Numerical solutions of two dimension
mixed Volterra- Fredholm integral equation of the second kind via Bernoulli collocation method.
Romanian Journal of Physics, 62(111), 1-11.
Hasan, T. I. Sulaiman N. A. and Saleh S. (2016). Aitken method on iterative kernel method for solving
system of Volterra-Fredholm integral equations of the second kind. Journal of Pure and Applied Sciences
(ZJPAS), 28(6), 79-88.
Jerri, A. J. (1985). Introduction to integral equations with applications. Marcel Dekker. New York and
Basel.
Mahmud, M.H. (2008). Approximation methods for solving system of linear two dimensional Fredholm
integral equations of a second kind. Master thesis Salahaddin University.
Mary C. (1979). Calculus and Analytic Geometry. Fifth edition, Addison Wesley publishing.
Mohammed K. S. (2015). Numerical Solution for Mixed Volterra-Fredholm Integral Equations of The
Second Kind By Using Bernstein Polynomials Method. Journal Mathematical Theory and Modeling.
5 (10), 154-162.
Saleh S., Hasan, T. I. and Sulaiman N. A. (2017). Fixed point and its improvement for the system of
Volterra-Fredholm integral equations of the second kind. Journal of Mathematica. 33(2), 191-206.
Tenwich, M. C. (2012). Error estimates for numerical solutions of one and two dimension Integral
equations, PhD Thesis, University of Leeds department of applied Mathematics.
Wazwaz, A.M. (2011). Linear and non-linear integral equations methods and applications. Springer-Verlag
Berlin Heidelberg.
Zhong C. Z. and Jiang W. (2012). An approximate solution for a mixed linear Volterra–Fredholm integral
Equation. Journal Applied Mathematics and letter, 25(1), 1131-1134.
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Published
2019-10-23
How to Cite
Hasan, T. I. (2019). An Approximate Solutions of two Dimension Linear Mixed Volterra- Fredholm Integral Equation of the Second Kind via Iterative Kernel Method. Journal of University of Raparin, 6(2), 101–110. https://doi.org/10.26750/paper
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Humanities & Social Sciences
