Valery Anatolievich Zhizneuski
Vitebsk State University,
Engineer Physics Dept.
PhD in phys. and math.
With a view of the construction of analytical solutions for boundary problems of electrodynamics of environments with spatio-temporal changes of parameters the approach based on the generalized Fourier method of variables separation has been developed. The improvement of this method, within the limits of the given work, is aimed at the over-coming of a mathematical problem of its practical use. The problem arises when solving overdetermined systems of ordinary differential equations which in a certain class of functions are equivalent to the original partial differential equation. The formed systems of the separated equations contain a large quantity of the coefficients defined from the compatibility condition. The proved theorems have allowed us to reduce the quantity of uncertain factors, and, hence, to reduce multivariability of construction of the solution. Taking into account the obtained results we offer the algorithm of application of the method to the solution of boundary problems with second order linear partial differential equations.