The Numerical Solution for Solving nth Order Integro-Differential Equations via Boubaker Scaling Functions

integro-differential equations,

Keywords: scaling function, integro-differential equations, collocation method

Abstract

In this paper, the continuous Boubaker scaling functions were constructed with the presentation on the interval [0,1], which obtained depending on Boubaker polynomials.

 In this current study the Boubaker scaling polynomial has been applied for solving the nth order integro–differential equations (IDE’s).

The collocation method with the aid of Boubaker scaling functions together were utilized to transform the higher order integro–differential equations into a problem of linear system algebraic equations.

     Some numerical examples were added to show the simplicity and accuracy of the proposed technique. The results have been compared with the exact solution using Matlab and illustrated by graphs.

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References

[1] David C. and Heil C., Characterizations of Scaling Functions: Continuous Solutions, SIAM, Vol.15, No.2, (1994).
[2] Ghaderpanah and S. Klasa, Polynomial Scaling, SIAM J. NUMER. Anal., Vol.27, No.1, pp. 117-135, February (1990)
[3] S.A. Yousefi, Legendre Scaling Function for Solving Generalized Emden- Folwer Equation, international journal of information and systems sciences, Vol.(3),No.(2),(2007).
[4] Suha S. and Amal M., An Efficient Algorithm for nth order Integro-Differential Equations Using New Haar Wavelet Matrix Designation, (IJETCAS), 12 -209,(2012).
[5] Fariborzi. M.A. and Daliri.S., Numerical Solution of Integro-Differential Equation by Using Chebyshev Wavelet Operational Matrix of Integration, international Journal mathematics and Computer, Vol.2 (2), (2012).
[6] Husein J., Omer A. and S. Al-Shara, Numerical Solution of Linear Integro-Differential Equations, Journal of mathematics and statistics4 (4), (2008).
[7] Galina M. , M. Imanova and Vagivf I., solving Volterra integro- differential equation by the second derivative methods, international journal of applied Mathematics and information sciences9,No.5,(2015).
[8] Asmaa A., An Algorithm for nth Order Integro-Differential Equations by Using Hermit Wavelet Functions, J. Baghdad for sci., Vol. (11), no. (3), (2014).
[9] Abubakar A. and Taiwo O.A., Integral Collocation Approximation Methods for the Numerical Solution of Higher-Orders Linear Fredholm-Volterra Integro-Differential Equations, American journal of computational and applied mathematics,4(4),(2014).
[10] M. Al-towaiq and Ahmed K., Modified Algorithm for Linear Integro-Differential Equations of the Second Kind, American journal of computational and applied mathematics, 7,(2017).
[11] Sara D.and Jalil R., Boubaker Polynomials Collocation Approach for Solving Systems of Nonlinear Volterra- Fredholm Integral Equations, Journal of Taibah university for science,11,(2017).
[12] Hammeda O. and Ahsan F. ,A Combination of the Orthogonal Polynomials with Least –Squares Method for Solving High-Orders Fredholm-Volterra Integro-Differential Equations, Al-Qadisiyah Journal of pure science, Vol.26(1),pp.20-38, (2021).
[13] Tinggang Zhao, B. K. Ben Mahmoud, Some New Properties of the Applied-Physics Related Boubaker Polynomials, Differential Equations and Control Processes, Vol. 30(1), pp.8-19, (2009).
[14] Gradimir V. M. and Dusan J., Some Properties of Boubaker Polynomials and Applications, AIP conference proceedings, Vol.1479 (1) pp.1050-1053,) 2012),
[15] Ahmed I. and el., Indirect Method for Optimal Control Problem Using Boubaker Polynomial, Baghdad Science Journal, Vol.13 (1), (2016).
[16] Eman Hassan, An Approximate Solution to Calculus of variational Problems Using Boubaker Polynomials, Baghdad Science Journal, Vol.15 (1),pp. 106-109,(2018).
[17] Eman Hassan, Numerical Methods for Solving Optimal Control Problems Using Scaling Boubaker function, Al-Qadisiyah Journal of pure science, Vol.25(2),pp.78-89, (2020).
Published
2022-02-14
How to Cite
Ouda, E. H. (2022). The Numerical Solution for Solving nth Order Integro-Differential Equations via Boubaker Scaling Functions. Al-Qadisiyah Journal of Pure Science, 27(1), Math 60-69. https://doi.org/10.29350/qjps.2022.27.1.1478
Section
Mathematics