Optimal Numerical Solution Of A Second Derivative Hybrid Block Backward Differentiation Formula For Forecasting Agricultural Production In Adamawa State, Nigeria

• Bakari I. Abba

  Department of Mathematics and Statistics,Federal University of Agriculture Mubi (FUAMB), Nigeria

  Author

• Sunday Babuba

  Department of Mathematics and Statistics,Federal University of Agriculture Mubi (FUAMB), Nigeria

  Author

• Saratu M. Ezekiel

  Department of Mathematics and Statistics,Federal University of Agriculture Mubi (FUAMB), Nigeria

  Author

• Jalaluddeen Usman

  Department of Agricultural Economics and Extension, Adamawa state University Mubi, Adamawa state Nigeria

  Author

This study presents optimal numerical solutions based on a second-derivative hybrid block backward differentiation formula to forecast agricultural production in Adamawa State, Nigeria. Agricultural production forcasting refers to the process of predicting future crop yields, livestock output, or overall agricultural productivity in the region using various tools and methods. These predictions are based on advanced numerical methods. Moreover, using advanced numerical method in agricultural production brings several significant benefits, particularly in improving decision- making, efficiency and sustainability. These methods are especially valuable when applied to forecasting, optimization and modelling complex agricultural systems. The research was carried out with the aim of developing and applying an advanced numerical method for forecasting agricultural production in Adamawa State. By applying computational methods and algorithms, farmers and agricultural experts can optimize crop yields and enhance overall efficiency in the agricultural sector. Technologies such as precision farming, weather forecasting, and data analysis can help make better-informed decisions, leading to increased productivity. In addition, the hybrid block backward differentiaon formula (BDF) is applied to agricultural production forecasting by formulating the production process as a system of differential equation. The method provides reliable numerical approximations, enabling accurate prediction of future agricultural output in Adamawa State. The order and error constant have been investigated. The convergence analysis reveals that the methods ???? = 4 and their block forms are A-stable. The newly constructed method are applied to Vander pol stiff ordinary differential equations arising from real life situation has shown that it is efficient and compare favourably with other existing methods and the exact solutions. The method is also efficient because from the graphical solutions, the approximate solution matched toward the exact solution. The policy implication of this research is that the application of this method to predict agricultural production in Adamawa State would serve as reliable computational tool for forecasting crop yields and assessing the impact of environmental and economic variables on production outcomes. 

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