Quick question about improved Euler's method

**steph3824** · February 17th 2010, 11:45 AM

I am trying to understand an example in my book and something isn't making sense to me. The problem is: Use the improved Euler method to calculate approximate values of the solution of the initial value problem $y'=1-t-4y, y(0)=1$ .

I have found that $F_0=5$ . Assuming that h=.025 we then get $f(t_0+h,y_0+hf_0)=5.475$ .

It is after this where I'm getting confused. The equation in my book is $y_n+1=y_n+(h/2)(f_n+f(t_n+h, y_n+hf_n))$ . Using this we get $y_1=1+(0.5)(5+5.475)(0.025)=1.1309375$ .

I cannot for the life of me figure out where the 0.5 is coming from. Can someone show me where it's coming from?

**steph3824** · February 17th 2010, 11:47 AM

NEVER MIND! I had a major brain fart there. I just realized that they turned the 1/2 into a .5

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