Symbolic differentiation algorithms for hyperbolic perturbation problems with Neumann conditions using asymptotic formulas and uniform difference schemes

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.