Projection methods for integral equations in epidemic

Abstract

In this paper numerical methods for mixed integral equations are presented. Studied equations arise in the mathematical modeling of the spatio‐temporal development of an epidemic. The general theory of these equations is given and used in the projection methods. Projection methods lead to a system of algebraic equations or to a system of Volterra integral equations. The considered theory is illustrated by numerical examples.

Pateikiami skaitiniai metodai mišrioms integralinems lygtims. Nagrinejamos lygtys modeliuoja epidemiju dinamika erdveje ir laike. Apżvelgta tokiu lygčiu bendroji teorija, ji panaudota projekciniuose metoduose. Projekciniai metodai leidžia suvesti uždavini i algebriniu lygčiu sistema arba i Volteros integralines lygtis. Nagrinejami metodai iliustruojami skaitiniais pavyzdžiais.

Key words:

• Mathematical model of an epidemic
• spread of the disease
• mixed integral equations
• Volterra integral operator
• projection method
• Galerkin type method