Numerical integration of autonomous and non-autonomous non-linear size-structured population models

Area of Science:

• Numerical analysis
• Mathematical biology
• Computational science

Background:

• Population dynamics are modeled using non-linear size-structured models.
• Numerical methods are crucial for solving these complex models efficiently.
• Assessing the efficiency of numerical schemes is vital for accurate population simulations.

Purpose of the Study:

• To conduct an efficiency study of numerical methods for autonomous and non-autonomous non-linear size-structured population models.
• To evaluate the characteristics scheme, Lax-Wendroff method, and box method.
• To analyze the impact of model complexity on numerical method performance.

Main Methods:

• Implementation and description of three numerical methods: characteristics scheme, Lax-Wendroff, and box method.
• Testing with five diverse problems including equilibrium, periodic solutions, and various growth functions.
• Multiple regression analysis to determine global error constants and assess scheme stability.

Main Results:

• The box method demonstrates efficiency, particularly for complex population model scenarios.
• Comparative analysis of errors and computational times (cpu-times) for each method.
• Identification of constants governing the leading terms of global errors for each scheme.

Conclusions:

• The box method is a robust and efficient numerical technique for non-linear size-structured population models.
• Understanding numerical scheme properties like stability is key to interpreting efficiency results.
• Convergence analysis of the box method confirms its suitability for these applications.