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Numerical methods for solving the second boundary value problem for a multidimensional Sobolev type equation. (Russian. English summary) Zbl 1496.65144

Summary: 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.

MSC:

65M22 Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35R09 Integro-partial differential equations
76A10 Viscoelastic fluids
35Q35 PDEs in connection with fluid mechanics
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