We consider the nonlocal boundary value problem for differenceequations(uk?uk?1)/τ+Auk=φk,1≤k≤N,Nτ=1, andu0=u[λ/τ]+φ,0<λ≤1, in anarbitrary Banach spaceEwith the strongly positive operatorA. The well-posedness of this nonlocal boundary value problemfor difference equations in various Banach spaces is studied. Inapplications, the stability and coercive stability estimates inH?lder norms for the solutions of the differencescheme of the mixed-type boundary value problems for theparabolic equations are obtained. Some results of numericalexperiments are given.
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机译：我们考虑差分方程（uk？uk？1）/τ+ Auk =φk，1≤k≤N，Nτ= 1，并且u0 = u [λ/τ] +φ，0 <λ≤1的非局部边值问题，在任意Banach空间E中具有强正算子A。研究了不同Banach空间中差分方程的非局部边值问题的适定性。在实际应用中，获得了抛物型方程混合型边值问题差分方案解的Hilder范式中的稳定性和矫顽稳定性估计。给出了数值实验的一些结果。
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