I'm trying to compute the numerical solution for a Predator-prey model with 3 equations. This is the model:

$$\frac{dx}{dt} =x(1-\frac{x}{k_1})-\frac{pxz}{1+ax+chy}\\ \frac{dy}{dt} =y(1-\frac{y}{k_2})-\frac{qyz}{1+ax+chy}\\ \frac{dz}{dt} =\frac{\epsilon(px+cqy)z}{1+ax+chy}-dz$$

So, I'm not sure about does the Runge Kutta method works here, because the solution depends on the time. I already know the expressions

$${\displaystyle y_{i+1}=y_{i}+{1 \over 6}h\left(k_{1}+2k_{2}+2k_{3}+k_{4}\right)}$$

but I'm not sure about how to compute the solution. May someone explain me how to calculate the coefficients $k_i$ for this problem?


closed as off-topic by Federico Poloni, user44191, Sean Lawton, Jan-Christoph Schlage-Puchta, Mark Wildon Mar 19 at 20:07

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "MathOverflow is for mathematicians to ask each other questions about their research. See Math.StackExchange to ask general questions in mathematics." – Federico Poloni, user44191, Sean Lawton, Mark Wildon
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ This isn't a research level math question, so it's not appropriate for mathoverflow. There are plenty of sources that explain this method, including wikipedia. $\endgroup$ – David Ketcheson Mar 18 at 7:01