Direct Method for Variational Problems Using Boubaker Wavelets
Main Article Content
Abstract
The wavelets have many applications in engineering and the sciences, especially mathematics. Recently, in 2021, the wavelet Boubaker (WB) polynomials were used for the first time to study their properties and applications in detail. They were also utilized for solving the Lane-Emden equation. The aim of this paper is to show the truncated Wavelet Boubaker polynomials for solving variation problems. In this research, the direct method using wavelets Boubaker was presented for solving variational problems. The method reduces the problem into a set of linear algebraic equations. The fundamental idea of this method for solving variation problems is to convert the problem of a function into one that involves a finite number of variables. Different numerical examples were given to demonstrate the applicability and validity of this method using the Matlab program. Also, the results of this technique were compared with the exact solution, and graphs were added to these examples to test the convergence of Wavelet Boubaker polynomials using this method.
Article Details
This work is licensed under a Creative Commons Attribution 4.0 International License.
licenseTermsHow to Cite
Publication Dates
References
Eman, H.; Najeeb, S.; Samaa, F., Boubaker Wavelets Functions: Properties and Applications, Baghdad science Journal, 2021, 18, 4, 1226-1233.
Mohammadi, R.; Alavi, A., Quadratic Spline Solution of Calculus of Variation Problems, J. App. Eng. Math., 2015, 5, 2, 276-285.
Razzaghi, M.; Yousefi, S., Legendre Wavelets Direct Method for Variational Problems, Elsevier, Mathematics and Computers in Simulation, 2000, 53, 185-192.
Ravindra, M., Direct Method for Solving Variational Problems Using Haar Wavelet, International Journal research & advance in Engineer ( IJMRAE), 2010, 2, III, 85-90.
Suha, Najeeb; Mohammed, R.; Ahmed R., Direct restarted Pell algorithm for Solving calculus of Variation Problems, Journal of Al-Qadisiyah for computer science and mathematics, 2021, 13, 2, 169-180.
Najeeb, S.; Abdalelah, A., Numerical Solution of Calculus of Variations by Using the Second Chebyshev Wavelets, Eng. & Tech. Journal, 2012, 30, 18, 3219-3229.
Ghasemi, M., On Using Cubic Spline for the Solution of Problems in Calculus of Variations, Springer science and Business Journal, 2016, 73, 685-710.
Zarebnia, M.; Birjandi, M., The Numerical Solution of Problems in Calculus of Variational Using B-Spline Collocation Method, Journal of Applied Mathematics, 2012, 2012, 1-10.
Mahdy, AM.; Youssef, E., Numerical Solution Technique for Solving Isoperimetric Variational Problems, international journal of modern physics C (IJMPC), 2021, 32, 1, 1-4.
Razzaghi, M.; Ordokhani, Y.; Haddadi, N., Direct Method for Variational Problems by Using Hybrid of Block-Pulse and Bernoulli Polynomials, Romanian Journal of Mathematics and Computer Science, 2012, 2, 1-17.
Ordokhani, Y., Direct Walsch-Hybrid Method for Variational Problems, International Journal of Nonlinear Science, 2012, 11, 1, 114-120.
Zina Alabacy, The Applications of Wavelets for BVPs and Signal Processing, journal Kufa, 2020, 7, 2, 10-15.
Rayal, A.; Sag R., Numerical study of Variational Problems Moving or Fixed Boundary Conditions by Muntz Wavelets, 2020, 28, 1-2.
Eman, H., An approximate Solution of some Variational Problems using Boubaker Polynomials, Baghdad science Journal, 2018, 15, 1, 106-110.
Kafash, B.; elavarkhalafi, A.; Karbassi, S.; Boubaker, K., A Numerical Approach for Solving Optimal Control Problems Using the Boubaker Polynomials Expansion Scheme, Jour. Interp. App. Sci. Res., Article ID jiasc-00033, 2018, 1-18.