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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: liv on June 21, 2010, 09:30:23 pm

Title: euler's methods- numerical solutions of differential equations
Post by: liv on June 21, 2010, 09:30:23 pm

can anyone explain this? i don't get why it is used.

and this may be a simple question, but how do you do:
using euler's method, approximate y(2) with i) h=0.5 and ii)0.2 for dy/dx=x/(sqrt(x^2+8), y(1)=3

Title: Re: euler's methods- numerical solutions of differential equations
Post by: Yitzi_K on June 21, 2010, 10:56:18 pm

Euler's Method: y_n+1 = y_n + h*f'(x_n)

So in this case, with h=0.5, y₂ = 3 + 0.5*1/3

That gives y₂ = 19/6, repeat that with the new values to find y₃, which is an approximation for y(2).

It's the same with steps of 0.2, it will just take 5 applications of Euler's method, each building on the last, until you've found y₆.