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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Specialist Mathematics => Topic started by: Halil on June 26, 2011, 05:23:34 pm

Title: Eurlers Method
Post by: Halil on June 26, 2011, 05:23:34 pm: Can anyone show me how to solve this with detailed working out? Who ever does it first will win a Specialist trophy :)

Use Euler's method to find y2 if
dy/dx = 1/x
, given that y0 = y (1) = 1 and h = 0.1.
Express your answer as a fraction.
Title: Re: Eurlers Method
Post by: moekamo on June 26, 2011, 05:51:53 pm: $y_1=y_0+hy'(x_0) = 1 + \frac{1}{10} \frac{1}{1} = \frac{11}{10}$

$y_2=y_1+hy'(x_1) = \frac{11}{10} + \frac{1}{10} \frac{1}{1+0.1} = \frac{11}{10} + \frac{1}{10}\frac{10}{11} = \frac{1}{10}\left ( 11+\frac{10}{11} \right ) = \frac{131}{110}$

hope the answer is right :D
Title: Re: Eurlers Method
Post by: Halil on June 26, 2011, 05:55:54 pm: Thank you specialist gun. :)
Its correct, though I dont have that formula, i have another two.
Appreciate your help :)
Title: Re: Eurlers Method
Post by: taiga on June 27, 2011, 01:42:50 am: for moekamo :p

(http://2.bp.blogspot.com/_9C_3Zx1XoVI/TA5G34FicOI/AAAAAAAAAHE/wt2iAC7wbsM/s1600/trophy.gif)

Halil which formulae did you have? a bit concerned that you have two formulas xD

what you're doing is starting at a point (xo), and finding the gradient at that point and therefore finding the y value at x1 by simply going up (or down) by whatever the gradient*step size tells you to do (and of course across to x1 from x0)