Abstract: The article suggests methodological approaches to the formation of constraints in mathematical physics problems and algorithms for the numerical solution of these problems. The ideas underlying the methodological approaches and computational algorithms overlap with the ideas of Trefftz method, boundary element methods and methods of boundary integral equations. This is natural, because I began to solve applied problems using these approaches. I knew well the strengths and weaknesses of these methods. Therefore, I conducted research in order to increase the efficiency and accuracy of these methods.
Keywords: Constraints problems, fictitious canonical domains, boundary elements, fictitious canonical domains, boundary integral equations, linear combinations algorithm, boundary condition problems