Well-Posedness of the Boundary Value Problem for Parabolic Equations in Difference Analogues of Spaces of Smooth Functions

摘要

The first and second orders of accuracy difference schemes for the approximate solutionsof the nonlocal boundary value problemv′(t)+Av(t)=f(t)(0≤t≤1),v(0)=v(λ)+μ,0<λ≤1,for differential equation in an arbitrary Banach spaceEwith the strongly positiveoperatorAare considered. The well-posedness of these difference schemes in differenceanalogues of spaces of smooth functions is established. In applications, thecoercive stability estimates for the solutions of difference schemes for the approximatesolutions of the nonlocal boundary value problem for parabolic equation areobtained.