Abstract
In a closed domain, a two-point boundary value problem for loaded parabolic equations is considered. The method of lines with respect to the variable x is used to solve this problem. As a result of this approach, a discretized problem is formulated. The discretized problem is reduced to a two-point boundary value problem for loaded differential equations (LDE). The solution of the resulting boundary value problem is performed using the parameterization method developed by professor Dzhumabaev. The study demonstrates the relationship between the boundary value problem for the loaded parabolic equation and the related discretized problem.