Numerical Solutions of Linear Abel Integral Equations Via Boubaker Polynomials Method
Keywords:Abel integral Eqs, Boubaker polynomial, Numerical solutions, Numerical method, Singular Voltarra Eq.
In this article, a numerical method based on Boubaker polynomials (BPs) was presented to solve the Linear Abel integral (LAI) Eqs of first and second types. The matrices were used to form the (LAI) Eq into a system of linear Eqs. To get Boubaker parameters, solve this system of Eqs using the Guess elimination method. To explain the results of this method, four examples have been provided and compared with the results of many methods mentioned in previous research. MATLAB R2018b program was used to perform all calculations and graphs.
Published Online First 20/10/2023
Wazwaz A-M. Linear and Nonlinear Integral Equations: Methods and Applications. Heidelberg Dordrecht London New-York: Springer; 638 p. 2011.
Ali MR, Mousa MM, Ma W-X. Solution of Nonlinear Volterra Integral Equations with Weakly Singular Kernel by Using the HOBW Method. Adv Math Phys. 2019; 2019: 1-10. https://doi.org/10.1155/2019/1705651
Vanani SK, Soleymani F. Tau approximate solution of weakly singular Volterra integral equations. Math Comput Model. 2013; 57(3-4): 494-502. https://doi.org/10.1016/j.mcm.2012.07.004
Bairwa R, Kumar A, Kumar D. An Efficient Computation Approach for Abel’s Integral Equations of the Second Kind. Sci Technol Asia. 2020; 25(1): 85-94. https://doi.org/10.14456/scitechasia.2020.9
Zarei E, Noeiaghdam S. Solving generalized Abel’s integral equations of the first and second kinds via Taylor-collocation method. . arXiv preprint arXiv 2018 Apr 231804.08571. https://doi.org/10.48550/arXiv.1804.08571
Maurya R, Devi V, Srivastava N, Singh V. An efficient and stable Lagrangian matrix approach to Abel integral and integro differential equations. Appl. Math. Comput. 2020; 374: 1-30. https://doi.org/10.1016/j.amc.2019.125005
Sakran MRA. Numerical solutions of integral and integro-differential equations using Chebyshev polynomials of the third kind. Appl Math Comput. 2019; 351: 66-82. https://doi.org/10.54287/gujsa.1093536
Abdullah JT. Approximate Numerical Solutions for Linear Volterra Integral Equations Using Touchard Polynomials. Baghdad Sci. J. 2020; 17(4):1241-1249. https://doi.org/10.21123/bsj.2020.17.4.1241
Daşcioğlu A, Salinan S. Comparison of the Orthogonal Polynomial Solutions for Fractional Integral Equations. Math. 2019; 7(1): 1-10. https://doi.org/10.3390/math7010059
Hamdan S, Qatanani N, Daraghmeh A. Numerical Techniques for Solving Linear Volterra Fractional Integral Equation. J Appl Math. 2019; 2019(1): 1-9. https://doi.org/10.1155/2019/5678103
Mundewadi RA, Kumbinarasaiah S. Numerical Solution of Abel s Integral Equations using Hermite Wavelet. Appl. Math nonlinear Sci. 2019; 4(2): 395-406. https://doi.org/10.2478/AMNS.2019.2.00037
Li C, Clarkson K. Babenko's approach to Abel's integral equations. Math. 2018; 6(3): 1-15. https://doi.org/10.3390/math6030032
Li C, Li C, Clarkson K. Several Results of Fractional Differential and Integral Equations in distribution. Math. 2018; 6(6): 1-19. https://doi.org/10.3390/math6060097
Zhang L, Huang J, Pan Y, Wen X. A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels. Complexity. 2019; 2019: 1-12. https://doi.org/10.1155/2019/4813802
Ouda EH. An Approximate Solution of some Variational Problems Using Boubaker Polynomials. Baghdad Sci J. 2018; 15(1):106-109. https://doi.org/10.21123/bsj.2018.15.1.0106
Ouda EH, A. New Approach for Solving Optimal Control Problems Using Normalized Boubaker Polynomials. Emirates J Eng Re. 2018; 23(4): 33-38.
Ahmed IN, Ouda EH. An Iterative Method for Solving Quadratic Optimal Control Problem Using Scaling Boubaker Polynomials.Open Sci J. 2020; 5(2):1-10. DOI: https://doi.org/10.23954/osj.v5i2.2538
Salih Yalcınbas S, Akkaya T. A numerical approach for solving linear integro-differential-difference equations with Boubaker polynomial bases. Ain Shams Eng J. 2012; 3(2): 153-161. https://doi.org/10.1016/j.asej.2012.02.004
Abdullah, J. T, Sweedan, B. N. and Abdllrazak, B.T, Numerical solutions of Abel integral equations via Touchard and Laguerre polynomials. IJNAA. 2021; 12(2): 1599-1609.
Abdullah, J. T, Ali, H. S, Laguerre and Touchard Polynomials for Linear Volterra Integral and Integro Differential Equations. Phys. Conf. Ser. 2020; 1591(1): 1-17
Abdelkawy MA, Ezz-Eldien SS, Amin AZM. A Jacobi Spectral Collocation Scheme for Solving Abel’s Integral Equations. Prog Fract Differ Appl. 2015;1:187-200. https://doi.org/10.12785/pfda/010304
Pandey RK, Singh OP, Singh VK. Efficient Algorithms to Solve Singular Integral Equations of Abel Type. Comput. Math Appl. 2009; 57: 664-676. https://doi.org/10.1016/j.camwa.2008.10.085
Singh KK, Pandey RK, Mandal BN, Dubey N. An Analytical Method for Solving Integral Equations of Abel Type. Procedia Eng. 2012; 38: 2726-2738. https://doi.org/10.1016/j.proeng.2012.06.319
Copyright (c) 2023 Baghdad Science Journal
This work is licensed under a Creative Commons Attribution 4.0 International License.