Design and implementation of a programming language for numerical computations

Numerical analysis is a fundamental tool for solving critical problems in many scientific and engineering disciplines, making a solid foundation in it crucial. Problems in fields like mathematics, engineering, and natural sciences are often represented using mathematical models and solved using numerical analysis methods. However, the mathematical operations required by numerical methods, when implemented in modern programming languages, often lead to large pieces of code that are complex and poorly readable. Special-purpose languages, on the other hand, handle these operations through library functions, offering poor integration with other programming environments, less flexibility and practice. This thesis focuses on the design and development of a programming language (called MxPL) that facilitates the programming of numerical analysis methods by providing some basic constructs and functions. The MxPL language supports a user-friendly, open-source, and mathematical notation-like syntax, for the implementation of numerical analysis methods. The study presents a formal grammar compatible with the usual representations of mathematics and linear algebra, and then develops a parser, verifier and interpreter. Its performance in coding complex numerical analysis methods is demonstrated on some program examples. A comparative analysis based on basic language features is made with modern programming languages.