Consider that math modeling following initial valu problem dy/dt=3-2t-0.5y, y(0)=1

Suman Cole 2021-01-16 Answered

Consider that math modeling following initial valu problem
dydt=32t0.5y,y(0)=1
We would liketo find an approximation solution with the step size h=0.05
What is the approximation of y(0.1)?

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Expert Answer

komunidadO
Answered 2021-01-17 Author has 86 answers

Given Initial Value Problem is:
dydt=32t0,5y,y(0)=1,t0=0
and step size h=0,05
Here f(t,y)=32t0,5y
f(tn1,yn1)=32tn10,5yn1
=32{t0+(n1)h}0,5yn1
Now we have t0=0andy0=1
for n=1 f(t0,y0)=32{0+(11)h}0,5
=32×00,5×1
=30,5
=2,5
y1=y0+hf(t0,y0)
=1+0,05×2,5
=1+0,125
=1,125
Now, t1=t0+(n1)h=0+(21)×0,05=0,05,f0|><n=2f0|><
n=2,
f(t1,y1)=32{t0+(n1)h}0,5y1
=32{0+(21)0,05}0,5×1,125
=32×0,050,5625
=30,10,05625
=2,3375
y2=y1=hf(t1,y1)
=1,125+0,05×2,3375
=1,125+0,1169[four 

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