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, vol.16, no.9, pp.1172-1180, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 16 Issue: 9
- Publication Date: 2026
- Journal Name: Turkish World Mathematical Society Journal of Applied and Engineering Mathematics
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
- Page Numbers: pp.1172-1180
- Keywords: asymptotic formulas, hyperbolic perturbation problems, uniform difference schemes
- Yıldız Technical University Affiliated: Yes
Abstract
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.