Symbolic Differential Algorithms for the Solution of Hyperbolic Perturbation Problems by Asymptotic Formulas and Uniform Difference Schemes
Trends in Mathematics, Springer International Publishing Ag, ss.159-168, 2026
- Yayın Türü: Kitapta Bölüm / Araştırma Kitabı
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/978-3-032-19532-6_20
- Yayınevi: Springer International Publishing Ag
- Sayfa Sayıları: ss.159-168
- Anahtar Kelimeler: Asymptotic formula, Cauchy problem, Hyperbolic equations, Uniform difference schemes
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
In this paper, we investigate asymptotic formulas and 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 propose a symbolic differentiation algorithm designed for the numerical solution of hyperbolic perturbation problems by using asymptotic formulas and uniform difference schemes. The symbolic differential algorithms are implemented by Matlab and the results of numerical experiments are presented.