What are the problems that may arise by the application of Euler method?
2 problems are described. One of them:
1.It is written that from from the convergence order it can be concluded that halving the error means halving the step-size and thus doubling the number of grid points. This leads to the doubling of computational costs which might cause an enormous effort.
Do we halve the step-size in Euler method? For my imagination for Euler method we just define a step size as we wish. As smaller we take as more precise will be our approximation. But where does "halving" come from? Where is my confusion?