SYMBOLIC DIFFERENTIATION ALGORITHMS FOR HYPERBOLIC PERTURBATION PROBLEMS WITH NEUMANN CONDITIONS USING ASYMPTOTIC FORMULAS AND UNIFORM DIFFERENCE SCHEMES
Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, cilt.16, sa.9, ss.1172-1180, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 16 Sayı: 9
- Basım Tarihi: 2026
- Dergi Adı: Turkish World Mathematical Society Journal of Applied and Engineering Mathematics
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Sayfa Sayıları: ss.1172-1180
- Anahtar Kelimeler: asymptotic formulas, hyperbolic perturbation problems, uniform difference schemes
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
In this paper, we investigate asymptotic formulas and ε-uniform difference schemes for the numerical solution of perturbation problems. Unfortunately, both of these numerical methods involving sine and cosine fitting operator functions, which depend on ρ (ρ=τ/ε, ε small parameter and τ stepsize in t), are highly challenging with the realization to use symbolic differential algorithms. We present a symbolic differentiation algorithm developed for the numerical solution of hyperbolic perturbation problems with Neumann boundary conditions, employing asymptotic formulas and ε-uniform difference schemes. The symbolic differential algorithms are implemented by Matlab, and the results of numerical experiments are presented.