We consider an efficient finite difference method solving of two-dimensional parabolic equations with nonlocal conditions. The specific feature the investigated problem is that condition contains values solution's derivatives at different points. prove stability this in energy norm. main all eigenvalues corresponding are positive. Results computational experiments presented.

This paper provides a theoretical and numerical comparison of classical first-order splitting methods for solving smooth convex optimization problems cocoercive equations. From point view, we compare convergence rates gradient descent, forward-backward, Peaceman-Rachford, Douglas-Rachford algorithms minimizing the sum two functions when one them is strongly convex. A similar given in more gener...

The Peaceman-Rachford alternating direction implicit (ADI) scheme for linear time-dependent Maxwell equations is analyzed on a heterogeneous cuboid. Due to discontinuities of the material parameters, solution less than H2-regular in space. For ADI scheme, we prove rigorous time-discrete error bound with convergence rate that half an order lower classical one. Our statement imposes only assumpti...