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These are replies submitted by Simon45

thank you very much

@Carl Love  thanks for the reply

@Carl Love can you explain why a correction is needed if the forecast already has a high order of accuracy(fourth)?



@Carl Love Thanks



I understand you, but this solution I get built-in team, and I need to get a solution by running

I need to get a tridiagonal matrix somehow.


the problem is, I don't know how to change

@Carl Love 

the advantage of the Milne method over the Runge-Kutta of the 4th order is a higher speed, which is provided by the fact that at one integration step for the Runge-Kutta of the 4th order it is necessary to perform the function of calculating the derivatives 4 times, and in the Milne method only 1 time.
In my implementation, the execution occurs 6 times, which ensures that the implementation will run at least 1.5 times slower than Runge-Kutta. Is there a way to fix this?

Doubts I have in this part of:

if abs(d[i+1]) < eps then y[i]:=y[i]:
else y[i]:=s[i];
end if: end do;

In theory, it is said that if the accuracy is not performed, it is necessary to reduce the step twice while it is necessary to find an intermediate reference point between the i-th and (i-1)-th.

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