ON UNIFORM DIFFERENCE SCHEMES AND ASYMPTOTIC FORMULAS FOR THE SOLUTION OF HYPERBOLIC NONLOCAL BOUNDARY VALUE PERTURBATION PROBLEMS

Ashyralyev A., YILDIRIM Ö.

Journal of Mathematical Sciences (United States), 2026 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s10958-026-08259-9
  • Dergi Adı: Journal of Mathematical Sciences (United States)
  • Derginin Tarandığı İndeksler: Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Asymptotic formula, Hyperbolic equations, Nonlocal boundary value problem, Uniform difference schemes
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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.