R-functions and software in scientific research, engineering, and education

A modern methodology of analysis of temperature, force, electromagnetic and other physico-mechanical fields is proposed. It is based on the joint use of the R-functions theory, algebra of differential tuples and the technique of implementing variational and projection methods of solving boundary-value problems. The theoretical results obtained realize a new technology of programming in mathematical physics, create an easily adaptable system of POLYE family for different computer platform, develop new high-level problem-oriented languages RL and DIFOR, and determine the principles of designing specialized device for hardware implementation of duple operations. Program and technique means have been proposed and developed for effective and operative solution of mathematical modelling problems.