The third boundary value problem for loaded differential Sobolev type equation and grid methods of their numerical implementation

11th International Conference on "Mesh methods for boundary-value problems and applications"

Beshtokov, M.K.H.^1

Kabardino-Balkarian State University, Institute of Physics and Mathematics, Kabardino-Balkar Republic, 173 Chernyshevskogo St., Nalchik

36000, Russia^1

关键词: A-priori estimates;    Differential problems;    Grid methods;    Numerical implementation;    Right-hand sides;    Sobolev-type equation;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012019/pdf
DOI  :  10.1088/1757-899X/158/1/012019

来源: IOP

【 摘 要 】

In this paper, we consider the third boundary value problem for loaded differential Sobolev type equation and grid methods of their numerical implementation. To solve the problem, a priori estimates in differential and difference settings are obtained. These a priori estimates imply uniqueness and stability of the solution with respect to the initial data and the right-hand side on the layer, as well as the convergence of the solution of each of the difference problem to the solution of the corresponding differential problem.