EXISTENCE AND SOLUTION OF THIRD-ORDER INTEGRO-DIFFERENTIAL EQUATIONS VIA HAAR WAVELET METHOD

Rohul Amin (), Kamal Shah, Muhammad Awais, Ibrahim Mahariq, Kottakkaran Sooppy Nisar and Wojciech Sumelka
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Rohul Amin: Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa 25120, Pakistan
Kamal Shah: Department of Mathematics and Sciences, Prince Sultan University, P. O. Box 66833, 11586 Riyadh, Saudi Arabia3Department of Mathematics, University of Malakand, Dir(L), 18000 Khyber Pakhtunkhwa, Pakistan
Muhammad Awais: Department of Mathematics, University of Peshawar, Khyber Pakhtunkhwa 25120, Pakistan
Ibrahim Mahariq: College of Engineering and Technology, American University of the Middle East, Kuwait
Kottakkaran Sooppy Nisar: Department of Mathematics, College of Sciences and Humanities, Prince Sattam bin Abdulaziz University, Al Kharj 16278, Saudi Arabia6School of Technology, Woxsen University, Hyderabad 502345, Telangana, India
Wojciech Sumelka: Institute of Structural Analysis, Poznan University of Technology, Piotrowo 5 Street, Poznan 60-965, Poland

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

Abstract: This paper is related to some qualitative results about the existence and uniqueness of a solution to a third-order problem by using a fixed point approach. Haar technique is applied for numerical solution of a third-order linear integro-differential equation (IDE) with initial conditions. In IDE, the third-order derivative is computed by Haar functions, and the integration is used to get the expression of second- and first-order derivatives, as well as an approximate solution. Some examples from the literature are used to verify the validity of the proposed method. Error analysis is performed. Also, comparison between the exact and numerical solutions at different collocation points (CPs) is derived. The convergence rate is recorded taking different numbers of CPs, which is approximately equal to 2.

Keywords: Qualitative Results; Fixed Point Approach; Haar Wavelet; Numerical Results (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400376

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