Chapter 3Euler’s method is defned by equation (4) on page 125 oF the text to beyn+1=yn+hf(xn,yn),n=0,1,2,... ,wheref(x, y)=5y. Starting with the given value oFy0= 1, we computey1=y0+h(5y0)=1+5h.We can then use this value to computey2to bey2=y1+h(5y1)=(1+5h)y1=(1+5h)2.Proceeding in this manner, we can generalize toyn:ynh)n.ReFerring back to our equation Forxnand using the given values oFx0=0andx1= 1 we fnd1=nh⇒n=1h.Substituting this back into the Formula Forynwe fnd the approximation to the initial valueproblemy0=5y,y(0) = 1atx= 1 to be (1 + 5h)1/h.3.In this initial value problem,f(x, y)=y,x0,andy0= 1. ±ormula (8) on page 127 oF thetext then becomesyn+1
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at Berkeley.