# Runge-Kutta Method Errors

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).

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#### 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.