NUMERICAL SOLUTIONS OF NONLINEAR DELAY INTEGRO-DIFFERENTIAL EQUATIONS USING HAAR WAVELET COLLOCATION METHOD

Fazli Hadi, Rohul Amin, Ilyas Khan, J. Alzahrani, K. S. Nisar, Amnah S. Al-Johani and Elsayed Tag Eldin
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Fazli Hadi: Department of Mathematics, University of Peshawar, KPK, Pakistan
Rohul Amin: Department of Mathematics, University of Peshawar, KPK, Pakistan
Ilyas Khan: ��Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia
J. Alzahrani: ��Department of Mathematics, College of Education, Majmmah University, Al-Majmaah 11952, Saudi Arabia
K. S. Nisar: �Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
Amnah S. Al-Johani: �Mathematics Department, Faculty of Science, University of Tabuk, Tabuk, Saudi Arabia
Elsayed Tag Eldin: ��Faculty of Engineering and Technology, Future University in Egypt, New Cairo 11835, Egypt

FRACTALS (fractals), 2023, vol. 31, issue 02, 1-12

Abstract: In this paper, Haar wavelet collocation method (HWCM) for nonlinear delay Volterra, delay Fredholm and delay Volterra–Fredholm Integro-Differential Equations (IDEs) are studied numerically using HWCM. This method is very useful for solving nonlinear IDEs. The technique (HWCM) reduced the given equations into a system of nonlinear algebraic equations. The nonlinear system is then solved by Broydens technique. Some numerical examples are taken from literature for the validation purpose, computational efficiency and convergence of the proposed method. The approximate solution is compared with the exact solution and the maximum absolute and mean square root errors are presented for each example in tables. The comparison between exact and approximate solution is shown in figures for each example. The results are compared with existing methods from the literature. The results exhibit that the HWCM is simple, precise and efficient.

Keywords: Haar Wavelet Collocation Method (HWCM); Nonlinear Delay Integro-Differential Equations; Broydens Technique; Numerical Solutions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X2340039X

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