#hw16.txt Andrew Lohr 30 March2014

BestAdams := proc(f,x,y,x1) local d,h,curmind,curmin,curminh,trueval:
trueval := evalf(subs(x=x1,rhs(dsolve({diff(y(x),x)=subs(y=y(x),f),y(0)=1},y(x))))):
curmin := infinity:
for d from 1 to 10 do
for h in [.1,.01,.001] do
if(abs(trueval - AAB(f,x,y,0,1,h,x1,FAB(d))[2][-1])<curmin) then
curmin :=abs(trueval - AAB(f,x,y,0,1,h,x1,FAB(d))[2][-1]):
curmind := d:
curminh:=h:
fi:
od:
od:
curmind,curminh,curmin:
end:

#for the three given queries, we get
#d = 2, h = 0.1e-2, error = 0.2513e-5
#d = 3, h = 0.1e-2, error = 0.2991e-3
#d = 3, h = 0.1e-2, error = 1.0971*10^8
#respectively


#evaluating e^100, with the expression
#GIRK(RK4, y, x, y, 0, 1, .1, 100)[2][-1]
# we get 3.806898591*10^43
#whereas 
#GIRK(GL, y, x, y, 0, 1, .1, 100)[2][-1]
#gets us 2.688079916*10^43
# which is much closer to the "true" value of 
#2.688117142*10^43