Explore BrainMass
Share

Runge-Kutta Method Errors

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

Question:
How does this compare with the theoretical rate of convergence of 0(H2). Explain your result as best as you can?

Data:
We used the Runge-Kutta method to solve
y'(x) = - y(x) + x^0.1[1.1 + x], y(0) = 0
whose solution is y(x) = x^1.1. We solved the equation on [0,5] and we printed the errors at x = 1,2,3,4,5. We used stepsize h-0.1, 0.05, 0.0024, 0.0125, 0.00625. We calculated the ratios by which the errors decrease when h is halved.

The ratios by which the errors decrease when h is halved (see attached).

© BrainMass Inc. brainmass.com March 22, 2019, 12:56 am ad1c9bdddf
https://brainmass.com/math/discrete-math/runge-kutta-method-errors-518041

Attachments

Solution Preview

The answer is (assuming your implementation is correct and your results are correct), that the results do not match to the theoretical prediction. Theory says O(h^2), but your ...

Solution Summary

The Runge-Kutta method errors are compared with theoretical rates of convergence.

$2.19