1
$\begingroup$

I am solving a nonlinear ODE with a regular singularity using MATLAB ODE45 or ODE113.

I am wondering what precision and accuracy they have and what one can say about the numerical error. The idea would be to write a statement like

"The solution was found by means of ODE45 which has an accuracy of...".

Improve this question
$\endgroup$
3
  • 1
    $\begingroup$ ODE113 does not use a Runge-Kutta method. $\endgroup$
    – David Ketcheson
    Nov 1, 2015 at 4:34
  • $\begingroup$ I know that but thanks for pointing that out. I could have written that it uses Adams-Bashforth-Moulton but the question about the accuracy would still apply to it... $\endgroup$
    – Hamurabi
    Nov 1, 2015 at 12:40
  • 1
    $\begingroup$ What I meant to imply is that the title of your question does not accurately reflect the content. $\endgroup$
    – David Ketcheson
    Nov 2, 2015 at 6:13

2 Answers 2

Reset to default
2
$\begingroup$

The RK4* method is a fourth-order method, meaning that the local truncation error is on the order of $O(h^5)$, while the total accumulated error is order $O(h^4)$.

Improve this answer
$\endgroup$
3
  • $\begingroup$ Thanks @Dmitry. Do you think that for a second order ODE with nonlinearity and regular singularity Runge-Kutta yields trustworthy results? $\endgroup$
    – Hamurabi
    Oct 30, 2015 at 13:15
  • 1
    $\begingroup$ NB: Dmitry's statement is valid only in the asymptotic convergence regime $h \rightarrow 0$ (i.e., when $h$ is sufficiently small). $\endgroup$
    – GoHokies
    Oct 30, 2015 at 13:41
  • 2
    $\begingroup$ In the most widely accepted terminology, the local truncation error of this method is actually $O(h^4)$. The one-step error is $O(h^5)$. $\endgroup$
    – David Ketcheson
    Nov 1, 2015 at 4:33
1
$\begingroup$

Since ODE45 uses adaptive stepping, you might want to mention the error tolerance (RelTol and AbsTol) used. There is some information in the odeset documentation.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.