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Well-Posedness of the Modified Crank-Nicholson Difference Schemes in C |
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PP: 543-554 |
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Author(s) |
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Allaberen Ashyralyev,
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Abstract |
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| In the present paper the modified Crank-Nicholson difference schemes for the approximate
solutions of the nonlocal boundary value problem
v0 (t) + Av(t) = f(t)(0 t 1); v(0) = v() + ; 0 < 1
for differential equations in an arbitrary Banach space E with the strongly positive
operator A are considered. The well-posedness of these difference schemes in C ; (E) and C ;
(E) spaces is established. In applications, the coercive stability estimates for
the solutions of difference schemes of the second order of accuracy over time and of an
arbitrary order of accuracy over space variables in the case of the nonlocal boundary
value problem for the 2mth-order multidimensional parabolic equation are obtained.
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