Author(s)

G. V. Druzhinin, I.M. Zakirov, NM. Bodunov

Abstract

On numerical analytical methods for solving boundary-value problems of continua based on invariant solutions of the basic equations of mathematical physics G.V. Druzhinin, I.M. Zakirov, N.M. Bodunov Kazan State Technical University, Russia Abstract In this paper, we suggest a unified approach to the construction of basic functions (eigenfunctions) in handling the problems of continua, cubature and quadrature problems, and also the problems on (hyper)surfaces approximation. We present the description of numerical analytical methods for obtaining the approximate solutions of inner and outer boundary-value problems of continua (both linear and nonlinear). The method is based on the expansion of invariant solutions of partial differential equations in series of the basic functions. Also presented is the linearization of partial differential equations and the reduction of nonlinear boundary-value problems to the systems of linear algebraic equations (SLAE) solvable for the coefficie

Keywords