A fourth-order method for numerical integration of age- and size-structured population models. (English) Zbl 1172.92026
Summary: In many applications of age- and size-structured population models, there is an interest in obtaining good approximations of the total population numbers rather than of their densities. Therefore, it is reasonable in such cases to solve numerically not the PDE model equations themselves, but rather their integral equivalents. For this purpose quadrature formulae are used in place of the integrals. Because quadratures can be designed with any order of accuracy, one can obtain numerical approximations of the solutions with very fast convergence. We present a general framework and a specific example of a fourth-order method based on composite Newton-Cotes quadratures for a size-structured population model.
MSC:
| 92D25 | Population dynamics (general) |
| 65D32 | Numerical quadrature and cubature formulas |
| 65R20 | Numerical methods for integral equations |
| 65D30 | Numerical integration |
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