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Chapter 3: Q 3.6-2E (page 129)

Show that when Euler鈥檚 method is used to approximate the solution of the initial value problem y'=-12y,y(0)=3,at x = 2, then the approximation with step size h is3(1-h2)2h .

Short Answer

Expert verified

Proved

Step by step solution

01

Apply Euler’s formula

Here y'=-12y,y(0)=3

Apply the Euler鈥檚 formula

yn+1=yn+hf(xn,yn)

In our case of differential equation our equation is

yn=3(1-h2)n

The interval is

b-an=2-0n=2nn=2h

02

substitute in the Euler’s formula 

Now,

y1=31-h2y2=31-h22...yn=31-h2nyn=31-h22h

Hence it is proved that yn=31-h22h

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