On computational analysis via fibonacci wavelet method for investigating some physical problems

In this work, we considered wavelet analysis and the application of the Fibonacci wavelet collocation method (FWCM) for solving partial differential equations (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.