Bounded solution of Cauchy type singular integral equation of the first kind using differential transform method
DOI:
https://doi.org/10.24297/jam.v14i1.7049Keywords:
Integral equation, Cauchy kernel, Degenerate kernelAbstract
In this paper, an efficient approximate solution for solving the Cauchy type singular integral equation of the first kind is presented. Bounded solution of the Cauchy type singular Integral equation is discussed. Two type of kernel, separable and convolution, are considered. The differential transform method is used in the solution. New theorems for transformation of Cauchy singular integrals are given with proofs. Approximate results are
shown to illustrate the efficiency and accuracy of the approximate solution.
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References
[1] Abdulkawi, M., A Numerical Solution of Singular Integral Equations. International Journal of Mathematics and Statistics, Volume 10, Number W11(2011), 69-76.
[2] M Abdulkawi and M. Y. H Akran., Unbounded solution of characteristic singular integral equation using differential transform method. Journal of Advances in
Mathematics 9 (7). (2014), 2869-2881.
[3] Amit, Setia., Numerical solution of various cases of Cauchy type singular integral equation. Applied Mathematics and Computation, 230 (2014), 200–207.
[6] Aytac, Arikoglu and Ibrahim, Ozkol., Solutions of integral and integro differential equation systems by using differential transform method. Computers and
Mathematics with Applications, 56 (2008), 2411–2417.
[7] A. Dezhborda, Taher Lotfia and Katayoun, Mahdiania., A new efficient method for a cases of the singular integral equation of the first kind. Journal of
Computational and Applied Mathematics, 15 (2014), 0377 – 0427.
[8] Chakrabarti, A. and Berghe, V.G., Approximate Solution of Singular Integral Equations. Appl. Math. Lett. 17 (2004), 553-559.
[9] Eshkuvatov, Z.K., Nik Long, N. M. A.and Abdulkawi, M., Approximate solution of singular integral equations of the first kind with Cauchy kernel. Appl.
Math. Lett. 22 (2009), 651-657.
[10] Eshkuvatov, Z.K. , Nik Long, N. M. A. and Abdulkawi, M., On the Semi-bounded Solution of Cauchy Type Singular Integral Equations of the First Kind.
European Journal of Pure and Applied Mathematics Vol. 2, No. 3 (2009), 462-472.
[11] Mohamed S. Akel and Hussein S. Hussein., Numerical treatment of solving singular integral equations by using Sinc approximations. Applied Mathematics and
Computation lett. 218 (2011), 3565-3573.
[12] Samah, M. Dardery and Mohamed, M. Allan., Polynomials for Solving a Class of Singular Integral Equations. Applied Mathematics lett. 5 (2014),
753-764.
[13] Lifanov, I.K. (1996). singular integral equations and discrete vortices. VSP BV, the Netherlands.
[14] Kanwal, R. P. (1997). Linear Integral Equations, Theory and Technique. Second Edition. Birkhauser. Boston.
[2] M Abdulkawi and M. Y. H Akran., Unbounded solution of characteristic singular integral equation using differential transform method. Journal of Advances in
Mathematics 9 (7). (2014), 2869-2881.
[3] Amit, Setia., Numerical solution of various cases of Cauchy type singular integral equation. Applied Mathematics and Computation, 230 (2014), 200–207.
[6] Aytac, Arikoglu and Ibrahim, Ozkol., Solutions of integral and integro differential equation systems by using differential transform method. Computers and
Mathematics with Applications, 56 (2008), 2411–2417.
[7] A. Dezhborda, Taher Lotfia and Katayoun, Mahdiania., A new efficient method for a cases of the singular integral equation of the first kind. Journal of
Computational and Applied Mathematics, 15 (2014), 0377 – 0427.
[8] Chakrabarti, A. and Berghe, V.G., Approximate Solution of Singular Integral Equations. Appl. Math. Lett. 17 (2004), 553-559.
[9] Eshkuvatov, Z.K., Nik Long, N. M. A.and Abdulkawi, M., Approximate solution of singular integral equations of the first kind with Cauchy kernel. Appl.
Math. Lett. 22 (2009), 651-657.
[10] Eshkuvatov, Z.K. , Nik Long, N. M. A. and Abdulkawi, M., On the Semi-bounded Solution of Cauchy Type Singular Integral Equations of the First Kind.
European Journal of Pure and Applied Mathematics Vol. 2, No. 3 (2009), 462-472.
[11] Mohamed S. Akel and Hussein S. Hussein., Numerical treatment of solving singular integral equations by using Sinc approximations. Applied Mathematics and
Computation lett. 218 (2011), 3565-3573.
[12] Samah, M. Dardery and Mohamed, M. Allan., Polynomials for Solving a Class of Singular Integral Equations. Applied Mathematics lett. 5 (2014),
753-764.
[13] Lifanov, I.K. (1996). singular integral equations and discrete vortices. VSP BV, the Netherlands.
[14] Kanwal, R. P. (1997). Linear Integral Equations, Theory and Technique. Second Edition. Birkhauser. Boston.
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Published
2018-04-30
How to Cite
Abdulkawi, M. (2018). Bounded solution of Cauchy type singular integral equation of the first kind using differential transform method. JOURNAL OF ADVANCES IN MATHEMATICS, 14(1), 7580–7595. https://doi.org/10.24297/jam.v14i1.7049
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