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Problem (6.22) can be approximated by the difference problem (6.23).
Now we will show stability for the difference problem (3.7 - 3.8 3.7 - 3.8
In this section, we test the performance of the difference problem (3.7), (3.8).
It is clear that the difference problem (3.7), (3.8) is a nonlinear problem.
From (2.3), (2.15), by the mean-value theorem, we conclude that satisfies the difference problem.
Indeed, if by contradiction, we assume that there exist two solutions and to (2.3), then by the mean-value theorem, the difference satisfies the difference problem (2.38).
Similar(51)
Introduce the difference problems (2.39).
The difference problems (58) and (59) can be rewritten in the matrix form (56).
The proofs of the estimates (32), (33) for the solutions of the difference problems (34), (38) are based on equation (11) and estimates (43), (44).
Under these conditions, we construct the difference problems, the solutions of which converge to the first and pure second derivatives of the exact solution with the order (O(h^{4})).
Then max_{overline{R}^{h}}vert u_{h}-uvert leq ch^{6}bigl(1+vert ln hvert bigr), (2.26) where (u_{h}) is the solution of the finite difference problem (2.14), and u is the exact solution of problem (2.1).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com