Sep 2026· Journal of Nonlinear, Complex and Data Science· 0 citations· 40 references
Abstract
Abstract Mathematics is the basis for various subjects in the fields of engineering, physics, commerce, and so on. Many real-life problems in engineering, physics, biology, and e-commerce are modeled with the help of mathematical equations that lead to real-life applications. Here, some real-life problems in the field of engineering and physics are discussed with the help of the Haar wavelet method (HWM). Here, the operational matrix of integration (OMI) is constructed using Haar wavelets in order to solve fractional ordinary differential equations (FODEs). With the aid of OMI, FODE is transformed into an algebraic equation system. Using the Newton–Raphson approach, the system is further solved to find the unknown Haar coefficients. The results produced can be visually represented using numerical tables and graphical representations. The results of the presented method, the ND Solver solution, and the exact solution have been compared. The numerical results show how accurate and efficient HWM is in solving the FODE. The mathematical program Mathematica has been used for numerical computations.
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