Perturbation Methods for Acoustic Systems with Interval Parameters

Abstract

The aim of the paper is to present a new algebraic system with strictly defined new interval numbers and specifically defined addition and multiplication operations. The new introduced interval numbers are called perturbation interval numbers and are defined as ordered couples of real numbers with specially defined addition and multiplication. It’s proved that the new algebraic system is imbedded into the system of real interval numbers and so perturbation interval numbers are generalization of real intervals. Some additional properties as subtraction, inversion and division are presented too, as well as extensions of elementary functions. Applications to numerical methods of interval sound decay and reverberation time analysis are discussed.