ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Numerical Methods for Solving the Second Boundary Value Problem for a Multidimensional Sobolev Type Equation


M. KH. Beshtokov

Department of Computational Methods,
Institute of Applied Mathematics and Automation, KBSC RAS
Address: Shortanova 89A, Nalchik, 360000, Russia
North-Caucasus Federal University,
North-Caucasus Center for Mathematical Research,
Address: Pushkin 1, Stavropol, 355017, Russia


The second boundary value problem is investigated for a multidimensional Sobolev-type differential equation with variable coefficients. The considered equation is reduced to an integro-differential equation of parabolic type with a small parameter. For an approximate solution of the obtained problem, a locally one-dimensional difference scheme is constructed. Using the method of energy inequalities, an a priori estimate is obtained for the solution of a locally one-dimensional difference scheme, which implies its stability and convergence. For a two-dimensional problem, an algorithm is constructed for the numerical solution of the second boundary value problem for a partial differential equation of Sobolev type.



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