On the convergence of locally one-dimensional schemes for one nonlocal boundary value problem
On the convergence of locally one-dimensional schemes for one nonlocal boundary value problem
(Russian, English abstract)
Siberian Electronic Mathematical Reports, 21, No. 2, pp. 1562-1577 (2024)
Abstract:
The paper considers the third boundary value problem for a multidimensional integro-differential equation with a non-local source in a $p$-dimensional parallelepiped. Locally one-dimensional difference schemes are constructed for the problem under consideration. Using the energy inequality method, an a priori estimate for the LOS solution was obtained and its convergence was proved.
Keywords: non-local boundary value problem, boundary conditions of the third kind, locally one-dimensional scheme, stability of the difference scheme, convergence of the difference scheme, approximation, a priori estimation.