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The third boundary value problem

We suppose that the boundary surface S is equipotential, that is, [Pg.30]

Inasmuch as the boundary surface is an equipotential surface for both potentials Ui and U2, their difference is also constant on this surface and correspondingly we can write [Pg.31]

boundary conditions (1.89) and (1.90) define the potential within the volume V up to some constant. Correspondingly, the third boundary value problem can be formulated as  [Pg.31]

Inside the volume the potential obeys Poisson s equation [Pg.31]

On the level surface S, surrounding this volume, we have [Pg.31]


Example 1. The third boundary-value problem for an ordinary second-order differential equation ... [Pg.82]

The statement of the third boundary-value problem on eigenvalues is... [Pg.108]

Example 2. The third boundary-value problem. Given the same grid u)j as in Example 1, we now consider the difference boundary-value problem of the third kind... [Pg.120]

Example 5 Consider now the third boundary-value problem (9). As in Example 2 of Section 1 it will be convenient to introduce the space = 0 , of the dimension A +1 consisting of all grid functions defined on the uniform ... [Pg.138]

It is easily seen from (19) and (20) that no values of yu(x) at the vertices of the rectangle appear in this matter. This feature has some influence on a proper choice of 7 . For the third boundary-value problem and the scheme of accuracy 0 h ) (see Section 5) the boundary 7 consists of all the nodes on the boundary of the rectangle including its vertices. [Pg.247]

The third boundary-value problem. For the moment, the statement of the problem is... [Pg.489]

Locally one-dimensional schemes find a wide range of applications in solving the third boundary-value problem. If, for example, G is a rectangle of sides /j and or a step-shaped domain, then equations (21) should be written not only at the inner nodes of the grid, but also on the appropriate boundaries. When the boundary condition du/dx = cr u- -v[ is imposed on the side = 0 of the rectangle 0 < < / , a = 1,2, the main idea... [Pg.617]

Fig. 1.8. (a) Dirichlet s problem, (b) Neumann s problem, (c) the third boundary value problem. [Pg.26]


See other pages where The third boundary value problem is mentioned: [Pg.30]    [Pg.138]    [Pg.329]    [Pg.335]    [Pg.337]   


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