On The Higher-Order Pantograph Type Delay Differential Equation Via Orthonormal Bernstein Polynomials
DOI:
https://doi.org/10.29304/jqcm.2020.12.3.704Keywords:
Orthonormal Bernstein, Delay generalized pantograph equations, Operational Matrix of DerivativeAbstract
In this study, a collocation method based on the truncated orthonormal Bernstein polynomial was adopted to obtain an approximate solution for the generalized pantograph equations with proportional delay under some initial conditions. The adopted method is based on transforming both of the generalized pantograph equations and the adopted conditions into matrix equation which corresponds to a system of linear algebraic equation. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments and then validated by Math lab 15 package
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References
[1] J. R. Ockendon and A. B. Tayler," The dynamic of a current collocation system for a an electric locomotive", Journal mathematical and physical sciences,(1971), 447-468.
[2] A. Kurt, S. Yalçınbaş and M. Sezer," Fibonacci collocation method for solving linear differential-difference equation", Journal mathematical and computational applications, 18(3)(2013),448-458.
[3] Ö. Kürkçü and M. Sezer," A numerical Approach for solving differential pantograph equation with mixed delays using Dikson polynomials of the second kind",Journal of Science and Arts, 3(44)(2018),667-680.
[4] A. Isah, C. Phang and P. Phang," collocation method based on Genocchi operational matrix for solving generalized fractional pantograph equations", International Journal of Differential Equations,2017 (2017),1-10.
[5] S. Yalcinbas, M. Aynigul and M.Sezer," A collocation method using Hermite polynomials for approximate solution of pantograph equations", Journal Science Direct, 348(2011), 1128-1139.
[6] I. Ahmad and A. Mukhtar," Stochastic approach for the solution of multi-pantograph differential equation arising in cell-growth model", Journal applied mathematics and computation, 261(2015),360-372.
[7] A. O. AL-JUBORY and S. H Salih," Normalization Bernstein for solving fractional linear Volterra-Integro differential equation” ,International journal of mathematical Archive , 8( 2017) , 1-7.
[8] M. M. Ali," A new operational matrix of derivative for orthonormal Bernstein polynomial's ", Baghdad Science Journal ,11(3)(2014).
[2] A. Kurt, S. Yalçınbaş and M. Sezer," Fibonacci collocation method for solving linear differential-difference equation", Journal mathematical and computational applications, 18(3)(2013),448-458.
[3] Ö. Kürkçü and M. Sezer," A numerical Approach for solving differential pantograph equation with mixed delays using Dikson polynomials of the second kind",Journal of Science and Arts, 3(44)(2018),667-680.
[4] A. Isah, C. Phang and P. Phang," collocation method based on Genocchi operational matrix for solving generalized fractional pantograph equations", International Journal of Differential Equations,2017 (2017),1-10.
[5] S. Yalcinbas, M. Aynigul and M.Sezer," A collocation method using Hermite polynomials for approximate solution of pantograph equations", Journal Science Direct, 348(2011), 1128-1139.
[6] I. Ahmad and A. Mukhtar," Stochastic approach for the solution of multi-pantograph differential equation arising in cell-growth model", Journal applied mathematics and computation, 261(2015),360-372.
[7] A. O. AL-JUBORY and S. H Salih," Normalization Bernstein for solving fractional linear Volterra-Integro differential equation” ,International journal of mathematical Archive , 8( 2017) , 1-7.
[8] M. M. Ali," A new operational matrix of derivative for orthonormal Bernstein polynomial's ", Baghdad Science Journal ,11(3)(2014).
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Published
2020-09-10
How to Cite
J. AL-Nasrawy, H. H., Al-Jubor, A. K. O., & Hussain, K. A. (2020). On The Higher-Order Pantograph Type Delay Differential Equation Via Orthonormal Bernstein Polynomials. Journal of Al-Qadisiyah for Computer Science and Mathematics, 12(3), Math Page 1– 14. https://doi.org/10.29304/jqcm.2020.12.3.704
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Math Articles
