THE METHOD OF STRAIGHT LINES IN THE APPLICATION TO CERTAIN BOUNDARY PROBLEMS (METOD PRYAMYKH V PRIMENENII K NEKOTORYM KRAEVYM ZADACHAM),
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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Before the middle 1930s the prevailing method of the numerical solution of boundary value problems was the method of finite differences. About 1935 there appeared, several works devoted to the solution of partial differential equations with two variables, the basic idea of which is the preservation of the method of finite differences only for one change so that the solution of partial differential equations would lead to the solution of the system of ordinary differential equations. The character of this system depends on both the form of the equation and on the type of boundary conditions of the problem. In earlier published works of L. V. Kantorovich the solution of partial differential equations is reduced to the solution of the system of differential equations obtained from other more general considerations. By analogy with the method of grids, it is natural to call the mentioned group of methods, the methods straight lines and lines. Calculations reported in this paper show the effectiveness of the method of straight lines, and therefore, the application of it for a numerical solution of boundary problems as expedient.
- Theoretical Mathematics