Oncomputationalanalysis via fibonacci wavelet method for investigating some physical problems
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Date
2025
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Abstract
In this work, we considered wavelet analysis and the application of the Fibonacci
waveletcollocationmethod(FWCM)forsolvingpartialdifferentialequations(PDEs).
The proposed technique starts with formulating Fibonacci wavelets using Fibonacci
polynomials. Subsequently, the spectral collocation technique is applied to convert the
given problem into a system of algebraic equations, which are then solved using the
Newton method. Error estimation and convergence analysis of the proposed scheme
are also investigated. The effectiveness and precision of the FWCM are demonstrated
through a comparative analysis with exact solutions and other existing methods in the
literature. The obtained results demonstrate that the proposed technique is an efficient
tool for solving PDEs and is also applicable for numerically examining similar types
of physical problems.