AN AGE-STRUCTURED POPULATION MODEL WITH STATE-DEPENDENT DELAY: DERIVATION AND NUMERICAL INTEGRATION

作者：Magpantay F M G^*; Kosovalic N; Wu J

来源：SIAM Journal on Numerical Analysis, 2014, 52(2): 735-756.

DOI：10.1137/120903622

• state-dependent delay differential equations
• age-structured population models
• method of characteristics
• numerical stability

We present an age-structured population model that accounts for complex life cycles and competition for resources limiting the transition to maturity. Taking all of these into account leads to a new mathematical model with a state-dependent delay that cannot be analyzed using the established framework of functional differential equations or directly simulated by standard numerical schemes for age-structured populations. In this paper we present the derivation of the model and a numerical scheme to integrate the equations. Convergence of the method is proven by verifying first consistency and then stability. The difficulties involved in this proof, as well as in the implementation of the scheme, stem from the state-dependent delay term. The numerical scheme is shown to be of order 2 in the given norm, and at least of order 3 2 in the supremum norm over the mesh point values.

• 出版日期2014