The differential-symbol method of constructing the quasi-polynomial solutions of two-point problem

Abstract

The solvability of the problem with local nonhomogeneous two-point in time conditions for a homogeneous PDE of the second order in time and infinite order in spatial variable in the case when the set of zeroes of the characteristic determinant is not empty and does not coincide with C is investigated. The existence of a solution of the problem in which the right-hand sides of the two-point conditions are quasi-polynomials is proved. We propose the differential-symbol method of constructing the solutions of the problem.

Simulation of the Propagation of Electromagnetic Oscillations by the Method of the Modified Equation of the Telegraph Line

“…Consider a two-point problem with two-point conditions in the form of a constant voltage applied along a line at the initial moment of time = 0 and at some other point in time = . Using the differential-symbol method [17][18][19][20], we can write a generalized solution of the two-point problem (3), (4) in the following form:…”