conservation

Location: http://people.sc.fsu.edu/~jburkardt/classes/math1902_2020/conservation/conservation.html

conservation looks at how certain physical laws require that some quantities be conserved over time; and how different ODE solvers perform in satisfying such conservation laws.

The notes:

• conservation.pdf
• conservation.tex

Matlab:

• euler.m, our Euler ODE solver.
• midpoint.m, the midpoint ODE solver.
• pendulum_deriv.m, the right hand side of the pendulum problem.
• pendulum_energy.m, returns the energy of the pendulum problem.
• pendulum_euler.m, solves the pendulum ODE using the Euler method.
• pendulum_midpoint.m, solves the pendulum ODE using the midpoint method.
• pendulum_parameters.m, returns the values of the pendulum parameters g, l, m, t0, y0.
• pendulum_rk2.m, solves the pendulum ODE using the RK2 method.
• pendulum_solution.m, the exact solution of the pendulum problem.
• predator_conserved.m, evaluates a conserved quantity for the predator-prey ODE system.
• predator_deriv.m, defines the derivatives associated with the predator-prey ODE system.
• predator_parameters.m, returns the values of the predator-prey parameters alpha, beta, gamma, delta.
• rk2.m, a second order Runge Kutta ODE solver.
• rk4.m, a fourth order Runge Kutta ODE solver.
• sir_conserved.m, evaluates a conserved quantity for the SIR ODE system.
• sir_deriv.m, defines the derivatives associated with the SIR ODE system.
• sir_euler.m, uses the Euler method to solve the SIR ODE.
• sir_parameters.m, returns the values of the SIR parameters alpha, beta, gamma, delta.
• sphere_conserved.m, evaluates the conserved quantity for the sphere ODE.
• sphere_deriv.m, the right hand side of the sphere ODE.
• sphere_euler.m, solve the SPHERE ODE using the Euler method.
• sphere_rk4.m, solve the SPHERE ODE using the RK4 method.

Images:

• conservation.png, an illustration of a conservation law.
• sir2_euler.png, a plot of the results of a SIR2 ODE.
• sphere_euler_plot.png, the Euler solution to the SPHERE ODE.
• sphere_euler_conserved.png, the conserved quantity from the Euler solution to the SPHERE ODE.
• sphere_euler_plot3d.png, a 3D plot of the Euler solution to the sphere ODE.
• sphere_rk4_plot3d.png, a 3D plot of the RK4 solution to the sphere ODE.
• wrecking_ball.png, an illustration of the pendulum problem.
• pendulum_euler_energy.png, the pendulum energy history as determined by the Euler method.
• pendulum_midpoint_energy.png, the pendulum energy history as determined by the midpoint method.
• pendulum_rk2_energy.png, the pendulum energy history as determined by the RK2 method.