Problem first boundary value

Solution estimation for difference bormdary-value problems by the elimination method. In tackling the first boundary-value problem difference equation (21) has the tridiagonal matrix of order TV — 1... 

Example 4. The first boundary-value problem for the heat conduction equation ... 

In such a setting it is required to find the values of the parameter A such that these homogeneous equations have nontrivial solutions y(x) 0. In contrast to the first boundary-value problem, here the parameter A enters not only the governing eqnation, but also the boundary conditions. The introduction of new sensible notations... 

Example 4 Consider the first boundary-value problem... 

In such a setting problem (9) turns out to be equivalent to the first boundary-value problem... 

We call the nodes, at which equation (1) is valid under conditions (2), inner nodes of the grid uj is the set of all inner nodes and ui = ui + y is the set of all grid nodes. The first boundary-value problem completely posed by conditions (l)-(3) plays a special role in the theory of equations (1). For instance, in the case of boundary conditions of the second or third kinds there are no boundary nodes for elliptic equations, that is, w = w. 

We concentrate primarily on the first boundary-value problem associated with equation- (3) in the rectangle D = Q < x < l,0[Pg.300]

In the forthcoming example the first boundary-value problem is posed for the heat conduction equation in the rectangle Go = 0 < < /, 0 <... 

Example 2 The statement of the first boundary-value problem for the parabolic equation with mixed derivatives in the parallelepiped Go = 0 < a < L, a =1,2,..., p is... 

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