METHOD OF LINES FOR A LOADED PARABOLIC EQUATION

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