main types operators different sequences physics applied problems https://doi.org/10.1007/s10891-017-1576-z The Boundary Function Method. Fundamentals partial differential equations Robin boundary conditions system problem fundamentals region 2021-11-01T18:31 form differential operators articles boundary functions https://scigraph.springernature.com/explorer/license/ sequence 366-391 The boundary function method is proposed for solving applied problems of mathematical physics in the region defined by a partial differential equation of the general form involving constant or variable coefficients with a Dirichlet, Neumann, or Robin boundary condition. In this method, the desired function is defined by a power polynomial, and a boundary function represented in the form of the desired function or its derivative at one of the boundary points is introduced. Different sequences of boundary equations have been set up with the use of differential operators. Systems of linear algebraic equations constructed on the basis of these sequences allow one to determine the coefficients of a power polynomial. Constitutive equations have been derived for initial boundary-value problems of all the main types. With these equations, an initial boundary-value problem is transformed into the Cauchy problem for the boundary function. The determination of the boundary function by its derivative with respect to the time coordinate completes the solution of the problem. function method coefficient general form mathematical physics 2017-03 false respect solution differential equations Dirichlet basis conditions 2017-03-01 constitutive equations boundary conditions method boundary-value problem boundary equations derivatives en use function Cauchy problem variable coefficients initial boundary-value problem boundary function method article point Neumann power polynomials time types boundary points algebraic equations determination linear algebraic equations equations polynomials dimensions_id pub.1085106214 Pure Mathematics A. V. Luikov Heat and Mass Transfer Institute, National Academy of Sciences of Belarus, 15 P. Brovka Str., 220072, Minsk, Belarus A. V. Luikov Heat and Mass Transfer Institute, National Academy of Sciences of Belarus, 15 P. Brovka Str., 220072, Minsk, Belarus Mathematical Sciences Numerical and Computational Mathematics 2 V. A. Kot Journal of Engineering Physics and Thermophysics 1062-0125 1573-871X Springer Nature 90 doi 10.1007/s10891-017-1576-z Springer Nature - SN SciGraph project