High-order IMEX-WENO finite volume approximation for nonlinear age-structured population model

ABSTRACT

In this article, we design a high-order implicit–explicit weighted non-oscillatory (IMEX-WENO) scheme for the solution of the population age density model with the nonlinear mortality rate as well as fertility rate. The mortality rate is the combination of natural mortality that comes to be unbounded at maximum age and bounded external mortality rate that includes external resources as well as seasonality. The existence of global terms in the mortality function as well as in the boundary condition is the main technical complication which provides high nonlinearity for the model equation. We carefully construct a numerical scheme in such way, that the high-order accuracy is maintained in the global terms and boundary condition. The performance of the designed scheme is shown by comparing with the exact solution of the examples considered.

KEYWORDS:

• Numerical methods
• finite maximum age
• modelling and simulation
• finite volume approximation
• IMEX-WENO

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65L04
• 65M08
• 92D25

Acknowledgements

We thank the anonymous reviewers for their careful reading of our manuscript and their many insightful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author is thankful to the University Grants Commission, Government of India (F. 2-16/2011(SA-I)) for providing financial assistance in terms of Senior Research Fellowship.