Application of monadic calculations in solving numerical problems

This work is a further development of research on the use of functional programming for numerical methods. In particular, functional programming can help port programs to graphics accelerators with CUDA technology. Previous work has focused on functors (and applicative functors). The theoretical foundations of monadic computing were outlined, but how they could be applied in practice was not discussed. This paper attempts to fill this gap. One of the basic principles of functional programming is function composition, which allows you to build complex functions from simple ones and, thus, simplifies the writing of complex programs. Monad calculations allow you to build chains of complex calculations. Such chains are also, in a sense, a composition of functions, but at a higher, monadic level (monadic composition).