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