Exploring the performance of ChatGPT for numerical solution of ordinary differential equations

Abstract

This study aims to evaluate ChatGPT’s capabilities in certain numerical analysis problem: solving ordinary differential equations. The methodology which is developed in order to conduct this research takes into account the following mathematical abilities (defined according to National Centre for Education Statistics): Conceptual Understanding, Procedural Knowledge, Problem Solving, and Application in Real-world Contexts. The outcomes demonstrate that ChatGPT’s performed very well for the set tasks, and it also gives promising results for programming code generation, with certain limitations. The effectiveness and accuracy of the answers and solutions obtained by ChatGPT are related to the type of equation, i.e., how complex it is, and also with the instructions we give to ChatGPT. It also requires further improvement of the machine learning model and the ability to provide an explanation of how the output was obtained.

Keywords

• artificial intelligence (ai), differential equations, numerical solution, chatgpt