Research Information System
Journal of Mathematical Sciences (United States), 2026 (Scopus)
The abstract nonlocal boundary value problem (Formula presented.) for hyperbolic equations in a Hilbert space H, where A is a self-adjoint positive definite operator and ε∈0,∞ is a parameter multiplying the highest-order derivative term, is considered. An asymptotic formula for the solution of this problem with a small ε parameter is established. The high order of accuracy two-step uniform difference scheme for the solution of this problem is presented. The convergence estimates for the solution of the difference scheme are obtained.