A Novel Hybrid Approach Leveraging Shehu Transformation, Akbari-Ganji’s Method, and Padé Approximant for the Resolution of Diffusive Prey-Predator Systems

Abstract

This study introduces a novel method aimed at deriving approximate solutions for diffusive prey-predator systems. The proposed method seeks to circumvent the limitations of extant techniques, which frequently grapple with obtaining accurate analytical solutions and managing intricate computational operations. This new approach amalgamates the Shehu transformation, Akbari-Ganji's method, and Padé Approximant to facilitate a more precise and efficient solution. The accuracy, efficiency, and effectiveness of the proposed method are assessed through the analysis of two exemplar cases in one-and two-dimensional spaces. Results gleaned from the novel method underscore its superior accuracy and efficiency compared to traditional methods used for approximating analytical solutions to similar problems. Further, the utilization of infographics and tables elucidates the significance, validity, and indispensability of the proposed approach. This research augments our comprehension of biological systems and their interactions with the environment, thereby presenting a valuable contribution to the academic discourse.