midpoint

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

midpoint introduces two new ODE solvers: the midpoint method, and MATLAB's built-in ode45().

The notes:

• midpoint.pdf
• midpoint.tex

Matlab:

• backward_euler.m, an ODE solver using the backward Euler method.
• euler.m, an ODE solver using the Euler method.
• exp_backward_euler.m, uses the backward Euler method on the exp ODE.
• exp_deriv.m, returns the right hand side of the exp ODE.
• exp_euler.m, uses the Euler method on the exp ODE.
• exp_midpoint.m, uses the midpoint method on the exp ODE.
• exp_ode45.m, uses ode45() on the exp ODE.
• exp_parameters.m, returns the parameters alpha, t0, y0 of the exp ODE.
• exp_solution.m, evaluates the solution of the exp ODE.
• midpoint.m, an ODE solver using the midpoint method.
• pendulum_deriv.m, returns the right hand side of the pendulum ODE.
• pendulum_energy.m, returns the energy of the pendulum ODE.
• pendulum_parameters.m, returns the parameters of the pendulum ODE.
• pendulum_solution.m, returns the solution of the pendulum ODE.
• predator_conserved.m, returns a conserved quantity of the predator ODE.
• predator_deriv.m, returns the right hand side of the predator ODE.
• predator_parameters.m, returns the parameters of the predator ODE.

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• quadex_backward_euler.m, uses the backward Euler method on the quadex ODE.
• quadex_deriv.m, returns the right hand side of the quadex ODE.
• quadex_midpoint.m, uses the midpoint method on the quadex ODE.
• quadex_solution.m, evaluates the solution of the quadex ODE.
• rms.m, evaluates the root mean square norm of a vector.
• stiff_deriv.m, returns the right hand side of the stiff ODE.
• stiff_midpoint.m, uses the implicit version of the midpoint method on the stiff ODE.
• stiff_midpoint_explicit.m, uses an explicit version of the midpoint method on the stiff ODE.
• stiff_solution.m, evaluates the solution of the stiff ODE.

Images:

• midpoint_image.png, a sketch of how the midpoint method works.
• quadex_backward_euler.png
• quadex_midpoint.png
• stiff_backward_euler_explicit.png
• stiff_midpoint.png
• stiff_midpoint_explicit.png
• vanderpol_ode45_plot.png