A HYBRID NUMERICAL TECHNIQUE FOR SOLVING THREE-DIMENSIONAL SECOND-ORDER PARABOLIC PARTIAL DIFFERENTIAL EQUATIONS

Muhammad Asif (), Rohul Amin (), Nadeem Haider (), Imran Khan (), Qasem M. Al-Mdallal and Salem Ben Said ()
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Muhammad Asif: Department of Mathematics, University of Peshawar, Peshawar, Pakistan
Rohul Amin: Department of Mathematics, University of Peshawar, Peshawar, Pakistan
Nadeem Haider: Department of Mathematics, University of Peshawar, Peshawar, Pakistan
Imran Khan: Department of Mathematics, University of Peshawar, Peshawar, Pakistan
Qasem M. Al-Mdallal: Department of Mathematical Sciences, UAE University, P. O. Box 15551, Al Ain, UAE
Salem Ben Said: Department of Mathematical Sciences, UAE University, P. O. Box 15551, Al Ain, UAE

FRACTALS (fractals), 2023, vol. 31, issue 02, 1-16

Abstract: In this paper, a hybrid approach is presented for the numerical solution of three-dimensional parabolic partial differential equations. This new approach is applicable to both linear and nonlinear parabolic problems including systems. This hybrid numerical technique is based on the Haar wavelet collocation technique and the finite difference method. In this technique, the space derivative is approximated by truncated Haar wavelet series whereas the time derivative is approximated by finite difference method. The aforementioned proposed algorithms are very simple and can easily be implemented in any computer-oriented language efficiently. In order to demonstrate the efficiency and better accuracy of the newly developed numerical technique it is applied to some well-known examples from previous literature that comprises linear and nonlinear three-dimensional parabolic equations including systems. The obtained results affirm better accuracy and widespread applicability of the newly proposed numerical technique for a range of benchmark problems.

Keywords: Haar Wavelets; Three-Dimensional Parabolic Partial Differential Equations; Collocation Method; Finite Difference Method (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1142/S0218348X23400182

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