error

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

error shows how we can try to estimate the error in our ODE approximation process using smaller steps or a higher order method.

The notes:

• error.pdf
• error.tex

MATLAB:

• expsin_deriv.m, defines the right hand side of the EXPSIN ODE.
• expsin_solution.m, defines the exact solution of the EXPSIN ODE.
• 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.
• rms.m, evaluates the RMS norm of a vector.

Images:

• desert_wander.png, an illustration of an erratic historic path suggests how useful an error-correction method can be.
• expsin_rk1_double_20.png, displays the n=20 expsin_rk1_double results.
• expsin_rk1_double_error_20.png, displays the estimated error for the n=20 expsin_rk1_double results.
• expsin_rk1_extrapolate_20.png, displays the n=20 expsin_rk1_extrapolate results.
• expsin_rk1_extrapolate_error_20.png, displays the estimated error for the n=20 expsin_rk1_extrapolate results.
• expsin_rk1_higher_20.png, displays the n=20 expsin_rk1_higher results.
• expsin_rk1_higher_error_20.png, displays the estimated error for the n=20 expsin_rk1_higher results.