(2)
(3)
(4)
|
Volume 1, 1997 |
14 |
In (5)-(8) the generally accepted notations are applied.
Let the problem (1)-(4) has the sufficiently smooth solution U. The following statement is true.
Theorem. The solution of the difference scheme (6)-(9) converges uniformly to the solution of the problem (1)-(4) and the rate of convergence is O(t +h1 +h2 ).
ON A COUPLING OF A FIRST ORDER HYPERBOLIC
AND SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS
D. Jaiani
I. Vekua Institute of Applied Mathematics
I. Javakhishvili Tbilisi State University
We consider a problem of coupling of a boundary value problem
| (1)
(2) (3) (4) |
|
and initial-boundary value problem
(5) (6) (7) (8) |
|
There are several possibilities of coupling. We consider two of them.
Lemma 1. The problem (1)-(8), where
(9) |
|
has infinite number of solutions.
Note that the uniqueness of solution of (1)-(9) can be ensured by the selection of interface boundary curve in a suitable way. For example, if an interface has a saw shaped form consisting of lines paralel to Ox axis and to characteristic lines of (5), then coupled problem (1)-(9) has unique solution.
