Effective Application of the Fourier Technique for Constructing a Solution to a Mixed Problem for a Telegraph Equation

An algorithm is presented for constructing and calculating a rapidly converging series that is a (generalized or classical) solution to a mixed problem for a telegraph equation considered in a half-strip. The case of an essentially non-self-adjoint operator with respect to the spatial variable is considered. The constructed series is a generalized d’Alembert formula. The proposed approach supersedes traditional variable separation for solving mixed problems, which usually results in slowly converging series.