Approximation method in one boundary problem with partial derivatives - Sinaisky, E. S. (Ukrains’kyi Matematychnyi Zhurnal, 1990)
The possibility is studied of jointly applying the Laplace transform and the a-method of V. K. Dzyadyk to construct an approximate solution of a boundary value problem in the case of a linear partial differential equation with coefficients of polynomial-type, depending on one independent variable. The existence and uniqueness is established of an approximate solution in the chosen form. An asymptotic evaluation of the approximation error is obtained.