About one parallel algorithm of solving non-local contact problem for parabolic equations

摘要

In the present work, the initial-boundary problem with non-local contact condition for heat (diffusion) equation is considered. For the stated problem, the existence and uniqueness of the solution is proved. The constructed iteration process allows one to reduce the solution of the initial non-classical problem to the solution of a sequence of classical Cauchy-Dirichlet problems. The convergence of the proposed iterative process is proved; the speed of convergence is estimated. The algorithm is suitable for parallel implementation. The specific problem is considered as an example and solved numerically.