Application of Monadic Calculations in Solving Numerical Problems

This paper continues our research on the application of functional programming to numerical methods. In particular, functional programming can help port programs to graphics accelerators that support CUDA. Our previous work was focused on functors (and applicative functors). The theoretical foundation of monadic calculations was outlined, so this paper focuses on their practical application. One of the basic principles of functional programming is function composition, which allows complex functions to be built from simple ones, thus facilitating the development of complex programs. Monads allow one to construct chains of complex computations. In a sense, these chains are also compositions of functions, but at a higher, monadic level (monadic composition).