Taylor collocation method for a system of nonlinear Volterra delay integro-differential equations with application to COVID-19 epidemic

Abstract

The present paper deals with the numerical solution for a general form of a system of nonlinear Volterra delay integro-differential equations (VDIDEs). The main purpose of this work is to provide a current numerical method based on the use of continuous collocation Taylor polynomials for the numerical solution of nonlinear VDIDEs systems. It is shown that this method is convergent. Numerical results will be presented to prove the validity and effectiveness of this convergent algorithm. We apply models to the COVID-19 epidemic in China, Spain, and Italy and one for the Predator–Prey model in mathematical ecology.

Keywords:

• Nonlinear Volterra delay integro-differential equations
• collocation method
• Taylor polynomials
• epidemic mathematical model
• corona virus

2010 Mathematics Subject Classifications:

• 45G15
• 34K28
• 45D05
• 45L05
• 65L60

Disclosure statement

No potential conflict of interest was reported by the author(s).