A Numerical Study of the Evolution of Smoking Habit Model Through Haar Wavelet Technique

The prosperity of a nation reflects many parameters such as natural resources, literacy, and population. Nowadays national wealth is its population’s health, and many bad habits affect the population. Smoking habit is one of them that harms society’s health. In this work, the numerical approximation of the evolution of the smoking habit model is studied and analyzed using the Haar wavelet collocation method (HWCM). Here, a system of fractional ordinary differential equations representing the smoking model is solved by building the operational matrix of integration (OMI) with the aid of Haar wavelets. A system of algebraic equations is created from the smoking model with the help of OMI. The system is further solved to extract the unknown Haar coefficients by applying the Newton–Raphson method. Numerical tables and graphical representations provide a visual representation of the obtained results. The results have been compared between the developed method, the ND Solver solution, and other methods in the literature. The numerical results demonstrate that how HWCM is highly precise and effective in solving the evolution of the smoking habit model. Numerical computations and implementation have been carried out using the mathematical software Mathematica.