The Task of Mathematical Modelling Using a Programming Language: A Scoping Review

BACKGROUND This study aims to explore the role of programming languages in the development and implementation of mathematical models, with a focus on the integration of advanced computing technologies. MATERIALS AND METHODS Utilising a narrative review method, the study methodically examines the body of research on mathematical modelling and the use of programming languages like Python, C++, and Julia. The performance of these languages is compared in a number of mathematical modelling tasks, such as numerical methods, linear algebra, and physical modelling. RESULTS The paper emphasises how cloud computing, artificial intelligence, and hybrid algorithms have significantly improved the precision and effectiveness of mathematical models. While C++ offers great performance in computationally demanding jobs but necessitates more development effort, Python has been demonstrated to be beneficial for speedy development because of its vast library ecosystem. Julia is a promising language for mathematical modelling because it strikes a compromise between usability and performance. The investigation also shows that the choice of computing methods and programming languages has a significant impact on the effectiveness of mathematical models. Every language offers advantages based on the particular modelling task, as shown by a thorough analysis of execution time, memory utilisation, and code size. Furthermore, the combination of quantum computing and machine learning offers fresh possibilities for resolving increasingly challenging issues that conventional approaches are unable to effectively handle. CONCLUSION According to the study’s findings, mathematical modelling will depend more and more on the cooperation of traditional approaches, contemporary programming languages, and cutting-edge technologies like artificial intelligence and quantum computing.