I am approximating a solution to a first order LODE using Euler's method. I made two tables, one using a step size of .01 and another using .05 ( I had to start at x=0 and end at x=1). I am not understanding the directions for the second part of my assignment:
It states that the order of numerical methods (like Euler's) is based upon the bound for the cummulative error; i.e. for the cummulative error at, say x=2, is bounded by $Ch^n$, where $C$ is a generally unknown constant and $n$ is the order. For Euler's method, plot the points: $(0.1, \phi(1)-y_{10}),$ $(.05, \phi(1)-y_{20}),$ $(.025, \phi(1)-y_{40}),$ $(.0125, \phi(1)-y_{80}),$ $(.00625, \phi(1)-y_{160})$ And then fit a line to the above data of the form $Ch$. I don't understand, am I supposed to plot these using a step size of .1 or .05? Or am I supposed to use another step size?
Any clarification is appreciated.
Thanks
Edit:
The LODE I am given is $y'=x+2y, y(0)=1$ and the exact solution I found was $\phi(x)=\frac{1}{4}(-2x+5e^{2x}-1)$.