A note on the difference schemes for hyperbolic-elliptic equations (Q2491408)

Summary: The nonlocal boundary value problem for the hyperbolic-elliptic equation \[ \begin{aligned} d^{2}u(t)/dt^{2}+ Au(t) = f(t), &\quad 0\leq t \leq 1,\\ -d^{2}u(t)/dt^{2}+ Au(t)=g(t), &\quad -1\leq t \leq 0, \end{aligned} \] \[ u(0)=\varphi, \qquad u(1)=u(-1) \] in a Hilbert space \(H\) is considered. The second order of accuracy of the difference schemes for the approximate solutions of this boundary value problem is presented. Stability estimates for the solution of these difference schemes are established.