(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
This article aims to develop a quick and easy Taylor wavelet collocation method with the help of an operational matrix of integration of the Taylor wavelets. Solving epidemiological models ensures the necessary accuracy for relatively small grid points. Finding the appropriate approximations with a new numerical design is challenging. This study examines the fractional Pine wilt disease (PWD) model. Using the Caputo fractional derivative for the fractional order, we developed the novel wavelet scheme known as the Taylor wavelet collocation technique (TWCM) to approximate the PWD model numerically. The results have been compared between the developed method, the Homotopy analysis transform method (HATM), the RK4 method, and the ND solver. The numerical outcomes demonstrate that (TWCM) is incredibly effective and precise for solving the PWD model of fractional order. The approach under consideration is a powerful tool for obtaining numerical solutions to fractional-order nonlinear differential equations. The fractional order differential operator provides a more advanced way to study the dynamic behavior of different complex systems than the integer order differential operator does. The proposed wavelet method suits solutions with sharp edge/jump discontinuities. Fractional differential equations, delay differential equations, and stiff systems can be solved using this method directly without using any control parameters. For highly nonlinear problems, the TWCM technique yields accurate solutions close to exact solutions by avoiding data rounding and just computing a few terms. Mathematical software Mathematica has been used for numerical computations and implementation.