convergence

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

convergence looks at computing and reporting convergence rates; log-log plots of convergence; the flame equation.

The notes:

• convergence.pdf
• convergence.tex

Matlab:

• flame_convergence_backward.m, does a convergence study for the flame ODE with the backward Euler method.
• flame_deriv.m, dydt = flame_deriv(t,y) evaluates the right hand side of the flame problem.
• flame_euler_backward.m, approximates the solution of the flame ODE using the backward Euler method.
• flame_exact.m, y=flame_exact(t,delta) returns the exact solution of the flame ODE at time t, with initial condition delta.
• rk4.m, a fourth-order Runge-Kutta ODE solver.
• stiff_convergence.m, does a convergence study for the stiff ODE with the Euler method.
• stiff_convergence_backward.m, does a convergence study for the stiff ODE with the backward Euler method.
• stiff_deriv.m, dydt = stiff_deriv(t,y) evaluates the right hand side of the stiff problem.
• stiff_euler.m, uses n equal steps of the (forward) Euler method to solve the stiff problem.
• stiff_euler_backward.m, uses n equal steps of the backward Euler method to solve the stiff problem.
• stiff_exact.m, y = stiff_exact(t) evaluates the exact solution of the stiff problem.

Images:

• convergence.png
• flame.png
• flame_convergence_backward.png
• stiff_convergence.png