SYMBOLIC DIFFERENTIATION ALGORITHMS FOR HYPERBOLIC PERTURBATION PROBLEMS WITH NEUMANN CONDITIONS USING ASYMPTOTIC FORMULAS AND UNIFORM DIFFERENCE SCHEMES

SYMBOLIC DIFFERENTIATION ALGORITHMS FOR HYPERBOLIC PERTURBATION PROBLEMS WITH NEUMANN CONDITIONS USING ASYMPTOTIC FORMULAS AND UNIFORM DIFFERENCE SCHEMES

A. Ashyralyev, O. Yildirim

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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.

Keywords

hyperbolic perturbation problems, asymptotic formulas, uniform difference schemes.