SOLVING MATHEMATICAL PROBLEMS USING EULER'S METHOD WITH ARTIFICIAL INTELLIGENCE

Аннотация

Euler's method is a fundamental numerical technique used for solving ordinary differential equations (ODEs), often applied in various scientific and engineering fields. Despite its simplicity, Euler's method can suffer from limitations in accuracy and stability, especially when dealing with complex or stiff differential equations. This paper explores the integration of Artificial Intelligence (AI) with Euler's method to enhance its performance. By leveraging machine learning models such as supervised learning, deep learning, and reinforcement learning, the step size, error prediction, and solution refinement can be dynamically optimized. AI techniques can also be used to adjust parameters and predict corrections, improving the overall accuracy and efficiency of solving mathematical problems. This fusion of AI and Euler’s method provides a promising approach to handling challenging differential equations with greater precision and reduced computational cost.