Информационная система "Конференции"

Abstracts

Numerical solution of differential and integral equations

In a bounded domain composed of two intervals, we consider a singularly perturbed boundary value problem for a quasilinear ordinary differential second-order equation. The highest derivative of the equation is multiplied by the perturbation parameter e taking arbitrary values from the half-interval (0,1]. The diffusion process is accompanied by convective transfer. The conjugation conditions are given on the interface boundary between the subdomains, which reflect the continuity of the concentration and of the generic (diffusion and convective) flow when passing across this boundary. As e → 0, the solution exhibits a boundary layer (in a neighbourhood of the outflow boundary) and a transient (interior) layer. The interior layer appears from that side of the interface boundary onto which the convective flow is directed.

For the problem under consideration we construct special difference schemes which converge uniformly with respect to the parameter e, that is, with errors in the numerical solutions which do not depend on the value of e. To construct these schemes, we use classical finite difference approximations on piecewise uniform meshes condensing in a neighbourhood of the boundary and interior layers. In particular, we construct domain decomposition schemes indended for parallel and sequential computations, where the number of iterations required for solving those schemes is independend of the parameter e. The domain decomposition schemes inherit the property of e-uniform convergence of the same order.

Note. Abstracts are published in author's edition

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