REPRODUCING KERNEL HILBERT SPACE METHOD FOR SOLVING ABEL’S INTEGRAL EQUATIONS
Maqola haqida umumiy ma'lumotlar
The Integration Equations are one of the significant & essential phenomena and abstractions for the sake of numerous types of problem-solving in mathematics and have had various applications in areas of different fields. In fact, have a high theoretical & applicability importance. Even so, in this Article, a detailed research is carried out into the “Abel Integral Equation” utilizing the Reproducing Kernel Hilbert Space Method (RKHS) which is one of the strong, concise & perfect methods particularly for simplification & solution of the Abel Integral Equation. The main purpose of this research is to seek the numerical solution for the Abel Integral Equation by RKHS Method.
[1] S. F. Javan, S. Abbasbandy, M. A. F.Araghi, Application of Reproducing Kernel Hilbert Space Method for Solving a Class of Nonlinear Integral Equations, J. Math Problems in Engineering. (2017) 1-10.
[2] C. Yang An efficient numerical method for solving Abel integral, J. Appl. Math and Compute. 227(2014) 656-661.
[3] S. Kumar. A. Kumar. D. Kumar, J. Singh, A. Singh, Analytical solution Integral Equations arising in astrophysics via Laplace transform, J. Egyptian. Mathematical Society. (2015) 23, 102-107.
[4] Bocher. M. ( 1974 ).Integral Equations. London: Cambridge University Press. 65- 201.
[5] R. P. Kanwal, Linear Integral Equations Theory and Technique New York: Academic Press. (1971) 8-172.
[6] M. Rahman. Integral Equations and their Applications. Southampton: WIT Pres (2007) 2-60.
[7] A. M. Wazwaz, Linear and Nonlinear Integral Equations Methods and Applications. New York: Springer. (2011) 12-41, 239-259.
[8] A. Alvandi, M. Paripour, The combined reproducing kernel method andTaylor series to solve nonlinear Abel’s integral equations with weakly Singular Kernel, Applied and interdisciplinary mathematics research article, Cogent Mathematics and Compute. (2016), 3:1250705.
[9] H. Beyrami, T. Lotfi, K. Mahdiani, Stability and error analysis of the Reproducing Kernel Hilbert space method for the solution of weakly Singular Volterra Integral Equation on graded mesh, Applied Numerical Mathematics, Published by Elsevier B.V.120 (2017) 197–214.
[10] A. Dezhbord, T. Lotfi, K. Mahdiani, A new efficient method for a cases the singular integral equation of the first, J. of Computational and Applied Mathematics, Islamic Azad University, Hamedan 65138, Iran S0377-0427(15)00481-1.
[11] M. Cui, Y. Lin, Nonlinear Numerical Analysis in Reproducing Kernel Space, Nova Science Pub, Inc. Hauppauge, (2008) 77-90
[12] K. Sadri, A. Amini, C. Cheng, Javan, A new operational method to solve Abel’s and Generalized Abel’s integral equations, J. Appl. Math and Computation. 137 (2017) 1-10.
[13] J. Biazar, M. A. Asadi, RBFs for Integral Equations with a Weakly Singular Kernel,Generalized Abel’s integral equations, American Journal of Applied Mathematics. Vol. 3, No. 6, (2015), pp. 250-255.
[14] M. A. Abdelkawy, Samer S. EEldien and A. Z. M. Amin, a Jacobi Spectral Collocation Scheme for Solving Abel’s Integral Equations, J. Progr. Fract. Differ. Appl. 1, No. 3, (2015) 187-200.
[15] M. Yaghobifar, N. M. A. Nik Long, Z. K. Eshkuvatov, Analytical-Approximate Solution Of Abel Integral Equations, J. International Mathematical Forum, Vol. 6, No. 5, (2011) 211 – 221.
[16] S. Kumar, Om P. Singh, S. Dixit, an Analytic Algorithm for Generalized Abel Integral Equation, J. Applied Mathematical Sciences, Vol. 5, no. 5, (2011) 223 – 232.
[17] S. A. Yousefi, Numerical solution of Abel’s integral equation by using Legendre wavelets Abel Integral Equation, J. Applied Mathematical and Computation, 175 (2006) 574–580.
[18] A. Shahsavaran, E. Babolian, Numerical implementation of an expansion method for Linear Volterra integral equations of the second kind with weakly singular kernels, J. International Applied Mathematical and Computation, Vol. 3(1), (2011) 1 – 8.
[19] A. M. Wazwaz, a Frist course in integral equations, Second Edition, World Scientific, New Jersey, Copyright (2015).
[20] A. Li, K. Clarkson, Babenko’s Approach to Abel’s Integral Equations, J. Mathematics Department of Mathematics and Computer Science, Brandon University, Brandon, MB R7A 6A9, Canada, (2018) 1 – 15.
Mehr, M. ., & Joya, H. . (2023). REPRODUCING KERNEL HILBERT SPACE METHOD FOR SOLVING ABEL’S INTEGRAL EQUATIONS. Academic Research in Educational Sciences, 4(11), 147–159. https://doi.org/
Mehr, Mehrullah, and Haji Ahmad Joya,. “REPRODUCING KERNEL HILBERT SPACE METHOD FOR SOLVING ABEL’S INTEGRAL EQUATIONS.” Academic Research in Educational Sciences, vol. 11, no. 4, 2023, pp. 147–159, https://doi.org/.
Mehr, . and Joya, . 2023. REPRODUCING KERNEL HILBERT SPACE METHOD FOR SOLVING ABEL’S INTEGRAL EQUATIONS. Academic Research in Educational Sciences. 11(4), pp.147–159.