ON UNIFORM DIFFERENCE SCHEMES AND ASYMPTOTIC FORMULAS FOR THE SOLUTION OF HYPERBOLIC NONLOCAL BOUNDARY VALUE PERTURBATION PROBLEMS
Journal of Mathematical Sciences (United States), vol.301, no.1, pp.1-22, 2026 (Scopus)
- Publication Type: Article / Article
- Volume: 301 Issue: 1
- Publication Date: 2026
- Doi Number: 10.1007/s10958-026-08259-9
- Journal Name: Journal of Mathematical Sciences (United States)
- Journal Indexes: Scopus, MathSciNet, zbMATH
- Page Numbers: pp.1-22
- Keywords: Asymptotic formula, Hyperbolic equations, Nonlocal boundary value problem, Uniform difference schemes
- Yıldız Technical University Affiliated: Yes
Abstract
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.