HERMITE WAVELET METHOD FOR APPROXIMATE SOLUTION OF HIGHER ORDER BOUNDARY VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS

Amanullah (), Muhammad Yousaf (), Salman Zeb (), Mohammad Akram (), Sardar Muhammad Hussain () and Jong-Suk Ro
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Amanullah: Department of Mathematics, University of Malakand, Chakdara, Dir Lower 18800, Pakistan
Muhammad Yousaf: Department of Mathematics, University of Malakand, Chakdara, Dir Lower 18800, Pakistan
Salman Zeb: Department of Mathematics, University of Malakand, Chakdara, Dir Lower 18800, Pakistan
Mohammad Akram: Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah 170, Saudi Arabia
Sardar Muhammad Hussain: Department of Mathematical Sciences, Balochistan University of Information Technology, Engineering and Management Sciences (BUITEMS), Quetta 87300, Pakistan
Jong-Suk Ro: School of Electrical and Electronics Engineering, Chung-Ang University, Dongjak-gu, Seoul 06974, Republic of Korea5Department of Intelligent Energy and Industry, Chung-Ang University, Dongjak-gu, Seoul, 06974, Republic of Korea

FRACTALS (fractals), 2023, vol. 31, issue 02, 1-15

Abstract: In this paper, Hermite wavelet method (HWM) is considered for numerical solution of 12- and 13-order boundary value problems (BVPs) of ordinary differential equations (ODEs). The proposed algorithm for HWM developed in Maple software converts the ODEs into an algebraic systems of equations. These algebraic equations are then solved by evaluating the unknown constants present in the system of equations and the approximate solution of the problem is obtained. Test problems are considered and their solutions are investigated using HWM-based algorithm. The obtained results from the test problems are compared with exact solution, and with other numerical methods solution in the existing literature. Results comparison are presented both graphically and in tabular form showing close agreement with exact solution, and greater accuracy than homotopy perturbation method (HPM) and differential transform method (DTM).

Keywords: Wavelet; Hermite Wavelet Method; Ordinary Differential Equations; Boundary Value Problems; Numerical Solutions (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400327

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