stepsize

Location: http://people.sc.fsu.edu/~jburkardt/classes/math1090_2020/stepsize/stepsize.html

stepsize looks at estimating the error, and adjusting the stepsize.

The notes:

• stepsize.pdf
• stepsize.tex

Matlab:

• expsin_exact.m, evaluates the exact solution of the expsin test problem.
• expsin_deriv.m, the right hand side of the expsin test problem.
• expsin_rk12_adapt.m, uses RK12 adaptive ODE integration on the expsin problem.
• expsin_rk12_error.m, uses RK12 ODE integration to compare errors on the expsin problem.
• flame_convergence_backward.m, does a convergence study for the flame ODE with the backward Euler method (corrected version).
• flame_convergence_euler.m, does a convergence study for the flame ODE with the forward Euler method.
• flame_deriv.m, dydt=flame_deriv(t,y) defines the derivative associated with the flame ODE.
• flame_euler.m, approximates the solution of the flame ODE using the forward Euler method.
• flame_euler_backward.m, approximates the solution of the flame ODE using the backward Euler method (corrected).
• flame_exact.m, y=flame_exact(t,delta) returns the exact solution of the flame ODE at time t, with initial condition delta.
• pendulum_conserved.m, the conserved quantity of the pendulum problem.
• pendulum_deriv.m, the right hand side of the pendulum problem.
• pendulum_euler_backward.m, [t,u,v]=pendulum_euler_backward(n) solves the pendulum ODE using the backward Euler method.
• pendulum_exact.m, the exact solution of the pendulum problem.
• pendulum_midpoint.m, [t,u,v]=pendulum_midpoint(n) solves the pendulum ODE using the midpoint method.
• pendulum_rk4.m, [t,u,v]=pendulum_rk4(n) solves the pendulum ODE using a 4th order Runge-Kutta method.
• rk1.m, the Euler method, written as a Runge Kutta ODE solver.
• rk12.m, the Euler/Heun methods, written as a pair of Runge Kutta ODE solvers, returning an error estimate.
• rk12_adapt.m, the Euler/Heun methods, written as a pair of Runge Kutta ODE solvers, using an adaptive stepsize.
• rk2.m, the Heun method, written as a Runge Kutta ODE solver.
• rk4.m, a fourth order Runge Kutta ODE solver.

Images:

• bad_step.png
• expsin_rk12_adapt.png
• expsin_rk12_error.png
• flame_convergence_euler.png