(untitled) (Computer systems and information technologies, 2025)
The study is dedicated to the comparative analysis of the computational performance of modern programming languages in the implementation of numerical methods for solving boundary value problems in mathematical physics. The central focus of the research is the Thomas algorithm – an efficient numerical method for solving systems of linear algebraic equations with a tridiagonal matrix. The research methodology is based on a unified implementation of the Thomas algorithm for each examined programming language, ensuring identical algorithmic logic. Experimental testing was conducted on systems with sizes ranging from 10⁵ to 1.5 × 10⁷ elements for programming languages including C, C++, C#, Java, JavaScript, Go, and Python, which represent different paradigms and approaches to computation. The obtained results demonstrate significant differences in the performance of various programming languages. It was established that low-level compiled languages exhibit the highest execution speed, especially for large problem sizes. In contrast, interpreted languages show significantly lower performance, which becomes more pronounced as the computational workload increases. The study experimentally confirmed the impact of compiler optimization modes on performance, revealing differences of up to 70% depending on the language and optimization level. The scientific novelty of this work lies in the comprehensive investigation of programming language performance in the context of numerical modeling by comparing their characteristics when solving mathematical problems. Future research will include an in-depth study of the impact of processor architecture, compiler optimization mechanisms, and runtime environment implementation on the performance of computational algorithms, as well as an expansion of the range of numerical methods and programming languages analyzed.