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practical08

practical08 - COSC 1002/1902 Computational Science in C...

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COSC 1002/1902 Computational Science in C Practical 8 This practical session involves numerically solving coupled systems of ordinary differential equations in C using the Runge-Kutta method. The exercises include models for ecosystems and nonlinear oscillators. Before you begin these exercises, you should review the material in lecture 8. The calculations in that lecture use the codes pred prey.c and pred prey mod1.c , which are available on the unit web pages. You can try compiling and running the codes yourself, to confirm the results obtained in lectures. If you succeed with this then you are ready to begin the exercises. If not consult a tutor, who can provide assistance. The exercises are for students in both units except where indicated (‘1002’ means that the question is just for students in COSC 1002, and ‘1902’ means that the question is just for students in COSC 1902). Remember to have a tutor mark off checkpoints as you reach them. Exercises 1. In lecture 8 the Lotka-Volterra model was introduced to describe predator-prey ecosystems. The deficiencies of the model were discussed, and two modified models were introduced. The first modified model is solved by the code pred_prey_mod1.c . The second modified model is described by the coupled ODEs dN dt = a 1 1 - N N * N - c 1 NP N + c 1 /b 1 , dP dt = a 2 P 1 - P b 2 N . (1) The detailed motivation for these equations was given in the lecture. Briefly, the first term on the right hand side of the ODE for N is logistic growth of the prey population (see Q2 in practical session 6). The second term describes the rate at which predators remove prey. For small prey numbers, this term is proportional to the predator population and to the prey population. For

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practical08 - COSC 1002/1902 Computational Science in C...

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