Modified Hermite Wavelet Discrete Matrix Approach for the Brusselator Chemical Model

The primary goal of this study is to create a wavelet collocation technique that can be used to solve nonlinear fractional order systems of ordinary differential equations, which are equations that arise in modeling problems related to auto-catalytic chemical reactions. Using the Hermite wavelet collocation method (HWCM), the system of nonlinear ordinary differential equations of integer and fractional order is numerically solved. The nonlinear Brusselator system is transformed into an algebraic equation system using the collocation method and the fractional derivative operational matrices. The Newton-Raphson method is used to solve these algebraic equations, and the approximate values of the derived unknown coefficients are substituted. Through the numerical examples, the method's computational effectiveness and correctness are illustrated with various model constraints. A numerical comparison is made between the current approach ND solver, RK method, and Haar wavelet method (HWM). The efficiency and reliability of the developed strategy's performance are shown in graphs and tables. The created Hermite wavelet collocation method is resilient and has good accuracy compared to current methods found in the literature. Numerical computations are performed through Mathematica, a mathematical software.