rk_answers

Matlab:

• expsin_deriv.m, defines the right hand side of the EXPSIN ODE.
• expsin_errors.m, compares the approximation errors of rk1, rk2 and rk4 on the EXPSIN ODE.
• expsin_rk1.m, uses rk1 (Euler method) to approximately solve the EXPSIN ODE.
• expsin_rk2.m, uses rk2 to approximately solve the EXPSIN ODE.
• expsin_solution.m, defines the exact solution of the EXPSIN ODE.
• predator_deriv.m, a function which defines the derivatives associated with the predator-prey ODE system.
• predator_rk1.m, a script to test the rk1 code with predator_deriv(), producing a solution, phase, and conservation plots.
• predator_rk2.m, a script to test the rk2 code with predator_deriv(), producing a solution, phase, and conservation plots.
• predator_rk4.m, a script to test the rk4 code with predator_deriv(), producing a solution, phase, and conservation plots.
• rk1.m, a Runge-Kutta ODE solver of order 1 (this is just the Euler method).
• rk2.m, a Runge-Kutta ODE solver of order 2.
• rk4.m, a Runge-Kutta ODE solver of order 4.
• rms.m, evaluates the RMS norm of a vector.

Images:

• expsin_rk1.png, the rk1 approximation of the EXPSIN ODE solution.
• expsin_rk2.png, the rk1 approximation of the EXPSIN ODE solution.
• predator_rk4_200.png, the rk4 approximation of the predator-prey solution.
• predator_rk4_conservation_200.png, the rk4 version of the predator-prey conservation plot.
• predator_rk4_phase_200.png, the rk4 version of the predator-prey phase plane.