COMPARATIVE ANALYSIS OF THE NUMERICAL SOLUTION OF THE DIFFUSION EQUATION IN PLANTS USING AUTOMATIC DIFFERENTIATION AND GRID METHODS

This paper presents a numerical investigation of the diffusion equation that models heat transfer in plant tissues, with a particular focus on a comparative analysis of two computational approaches: automatic differentiation and the classical grid-based finite difference method. Diffusive transport is a fundamental mechanism in plant physiology, especially under extreme environmental conditions where the efficiency of heat and mass exchange plays a critical role in plant survival and adaptation. The primary objective of this study is to evaluate and compare the accuracy, computational efficiency, and stability of the two methods in solving a one-dimensional heat transfer model. The problem is formulated alongside a numerical experiment in which solutions obtained via automatic differentiation—implemented within machine learning frameworks—are benchmarked against results produced by the traditional finite difference approach. The findings underscore the strengths and limitations of each method within the context of biophysical modeling. Furthermore, the results suggest a promising potential for integrating both approaches into hybrid computational schemes to enhance the analysis of thermal and diffusive phenomena in biological systems.