How do I calculate the effective order of a numerical method given a table of: number of steps, stepsize, approximate solutions at t=0, and approximate error?

Question

anonymous · Answer

Can you do a concrete example first?

anonymous · Answer

I'm not too sure what you mean? But the data in the table is like: 
Number of steps: 4, 8, 16, 32; Stepsize: 0.25, 0.125, 0.625, 0.03125; Approximate solution: 2.09599258, 2.09716632, 2.09725725, 2.09726358; Approximate error: 1.27x10-3, 9.77x10-5, 6.77x10-6, 4.46x10-7.