anonymous
  • anonymous
5. Consider the differential equation dy/dt= y − t. (a) Work out by hand three steps of Euler’s method with step size .25 for the above equation, with y(1) = 1.
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
Euler’s method is a method that's used to approximate solutions of initial value problems of the form \(y'=f(t,y), y(t_0)=y_0\). In each iteration you should apply \(y_{n+1}=y_n+hf(t_n,y_n)\), where h is the step size. I will help you with the first iteration on the next post.
anonymous
  • anonymous
Before I start, you need to notice that \(f(t,y)=y-t\). Iteration#1 (\(n=0)\): In this iteration we have \(y_n=y_0=1, t_n=t_0=1, \) and \(f(t_n,y_n)=f(t_0,y_0)=0.\) Hence \(y_1=y_0+hf(t_0,y_0)=1+0.25(0)=1\)
anonymous
  • anonymous
You might want to watch this video here http://www.youtube.com/watch?v=4CqaepeaJHA

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