Error Analysis and Stability of Numerical Methods for Solving Fractional Differential Equations in Biophysical Modeling

Saif Abdulkareem Mari  Al-Qaraghuli

Saif Abdulkareem Mari Al-Qaraghuli University of Kashan, Iran

Keywords: Fractional Differential Equations (FDEs), Numerical Methods, Biophysical Modeling

Abstract

Fractional differential equations (FDEs) have eCombined as a powerful tool for Representationing Complicated biophysical phenomena such as anomalous diffusion and viscoelastic behavior due to their ability to capture memory effects and hereditary properties. notwithstanding reAnswer fdes numerically presents important challenges including Problems of truth constancy and computational Productivity. This paper addresses these challenges by proposing and analyzing a novel numerical method tailored for solving FDEs in biophysical contexts. the wise employs amp limited limited Disagreement access with accommodative time-stepping ensuring both great truth and constancy spell maintaining computational feasibleness. A rigorous theoretical analysis is conducted to establish error estimates and stability conditions demonstrating the method consistency and convergence properties. quantitative experiments are performed along pragmatic biophysical problems such as arsenic abnormal dissemination inch tProblems and elastic matter distortion to corroborate the method operation. The results show that the proposed scheme achieves first-order temporal Precision and second-order spatial Precision outperforming standard techniques like the Grünwald-Letnikov method in terms of both precision and Productivity. Furthermore, the wise exhibits iron constancy low variable down orders and measure sizes devising it good for long Imitations of biophysical systems. These findings underscore the potential of the proposed approach to advance our understanding of Complicated biological Methods and Improve Foretelling Representation Ing in biophysics. away addressing name limitations of present methods this read Adds to the evolution of true and prompt quantitative tools for reAnswer fdes inch pragmatic Uses.

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