On Second Order of Accuracy Difference Scheme of the Approximate Solution of Nonlocal Elliptic-Parabolic Problems

and Applied Analysis 3 exist and are bounded for a self-adjoint positive operator A. Here B 1 2 ( τA √ A 4 τ2A ) , K ( I 2τA 5 4 τA 2 )−1 . 2.2 Theorem 2.1. For any gk, 1 ≤ k ≤ N − 1, and fk,−N 1 ≤ k ≤ 0, the solution of problem 1.2 exists and the following formula holds: uk ( I − R2N )−1{[ R − R2N−k ] u0 [ RN−k − R k ][ Pu0 − τ 0 ∑ s −N 1 P N−1Gfs μ ] − [ RN−k − R k ] I τB 2I τB −1B−1 N−1 ∑ s 1 [ RN−s − R s ] gsτ } I τB 2I τB −1B−1 N−1 ∑ s 1 [ R|k−s| − R s ] gsτ, 1 ≤ k ≤ N, 2.3