Numerical Approximation of the Fractional Pine Wilt Disease Model via Taylor Wavelet Collocation Method (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 theTaylor wavelets. Solving epidemiological models ensures the necessary accuracy for relatively small grid points. Finding the appropriate approximationswith a new numerical design is challenging. This study examines the fractionalPine wilt disease (PWD) model. Using the Caputo fractional derivative forthe fractional order, we developed the novel wavelet scheme known as the Taylor wavelet collocation technique (TWCM) to approximate the PWD modelnumerically. The results have been compared between the developed method,the Homotopy analysis transform method (HATM), the RK4 method, and theND solver. The numerical outcomes demonstrate that (TWCM) is incrediblyeffective and precise for solving the PWD model of fractional order. The approach under consideration is a powerful tool for obtaining numerical solutionsto fractional-order nonlinear differential equations. The fractional order differential operator provides a more advanced way to study the dynamic behaviorof 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 stiffsystems can be solved using this method directly without using any controlparameters. For highly nonlinear problems, the TWCM technique yields accurate solutions close to exact solutions by avoiding data rounding and justcomputing a few terms. Mathematical software Mathematica has been usedfor numerical computations and implementation.