Theoretical and numerical study of profit in agricultural sector model using wavelet method

Abstract

Agriculture is crucial in India’s economy and society, supporting rural livelihood and national food security. India is one of the world’s largest agricultural producers, with diverse crops and farming practices. This work aims to present the Chebyshev wavelet collocation method (CWCM) for assessing and producing a numerical approximation of profit in a fractional-order agriculture sector model. Together, numerical simulations and mathematical modeling analysis enhance agricultural management and understanding while offering crucial insights into the dynamics of agricultural profit. Numerical results are obtained from a mathematical and financial perspective using the model parameters for model validation. Additionally, the error and convergence analysis of the Chebyshev wavelets has been presented to assess the applicability of the proposed approach. This study aims to construct Chebyshev wavelet operational matrix of integration (OMIs) and apply them to the numerical solution of fractional differential equations representing the agriculture model. The operational matrices are used to simplify fractional differential equations to an algebraic system of equations. Finally, we graphically depict the results and offer empirical support for our theoretical conclusions through graphic representations. The CWCM approach generates precise results with better absolute error (Ae) for highly nonlinear scenarios by computing a small number of terms and avoiding data rounding. The results of the developed method, the RK4 method, and the ND solver have been compared. The numerical findings demonstrate how well (CWCM) solves the fractional order agriculture model in terms of accuracy and efficiency. Mathematica is a mathematical program used for numerical calculations and implementation.