abstract 31


31
On solution of a nonlocal problem with dynamic boundary conditions for a loaded linear parabolic equation by straight-line methods
Zakir Khankishiyev

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.

Keywords: Nonlocal problem, loaded parabolic equation, dynamic boundary condition, straight lines method, numerical solution, maximum principle, rate of convergence

Cite this paper:
Khankishiyev Z., On solution of a nonlocal problem with dynamic boundary conditionsfor a loaded linear  parabolic equation by straight-line methods.
Bull. Comput. Appl. Math. (Bull CompAMa),
Vol. 5, No. 1, Jan-Jun, pp.77-98, 2017