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

• Main Author: Zakir Khankishiyev
• Format: Article
• Language: English
• Published: Universidad Simón Bolívar 2017-02-01
• Series: Bulletin of Computational Applied Mathematics
• Subjects: Nonlocal problem; loaded parabolic equation; dynamic boundary condition; straight lines method; numerical solution; maximum principle; rate of convergence
• Online Access: http://drive.google.com/open?id=0B5GyVVQ6O030bWlzWkZHdlBsT1k
• ISSN: 2244-8659; 2244-8659

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.