After the war Rvachov was able to resume his studies at the University of Lviv, from where he graduated in 1952 and where, three years later, attained his first doctorate with a work on elastic theory.
He summarized his findings in a monograph (1982) which did not gain international recognition until Victor L. Shapiro’s English edition appeared six years later.
[3] With R-functions there appears the possibility of creating a constructive mathematical tool which incorporates the capabilities of classical continuous analysis and logic algebra.
In contrast to widely used methods of the network type (finite difference, finite and boundary elements), in the R-functions method all the geometric information present in the boundary value problem statement is reduced to analytical form, which allows one to search for a solution in the form of formulae called solution structures containing some indefinite functional components.
[4] Rvachov therefore provided computational mechanics with a new form of mathematical foundation with considerable heuristic potential.