On solution of a nonlocal problem with dynamic boundary conditions for a loaded linear parabolic equation by straight-line methods

We consider a nonlocal problem with dynamic boundary conditions for a loaded linear parabolic equation. For this problem we prove the unique solvability in Sobolev's spaces and the maximum principle under some natural conditions. We suggest the numerical straight-lines method for the finding of the solution of the problem. The convergence of the straight-lines method to the exact solution is also proved.