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Abstract

This study aims to present the modified Chebyshev wavelet collocation method (CWCM) to investigate and obtain the numerical approximation of CO2 emissions from the energy sector utilizing the fractional mathematical model. The need for energy rises as the population grows. Burning fossil fuels produces a significant portion of the world’s energy, which raises the atmospheric concentration of CO2 and causes global warming. The combination of mathematical modeling studies and numerical simulations allows us to understand the CO2 emissions from the energy sector. Our objective is to build an operational matrix of integration (OMI) based on Chebyshev wavelets and use it to the numerical solution of the CO2 emanation from the energy sector model. Furthermore, these OMI are used to simplify fractional differential equations into an algebraic equation system. Lastly, graphic representations are used to visually present the results and provide empirical support for our theoretical conclusions. Because the CWCM method computes only a few terms and avoids rounding data, it produces correct answers for highly nonlinear situations. We compared the outcomes of the RK4 technique, the ND solver, and the devised method. The numerical results show that CWCM solves the emanation of CO2 from the energy sector with remarkable accuracy and efficiency in both mathematical and environment view. Software called Mathematica has been used for numerical implementation and calculations.

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