dA/dt=0.5*A*(1−A/100)−10 with A(0)=70 and we want to use Euler's method to get an approximate value for A(10), with a step size of 1.

Jamarcus Lindsey 2022-09-30 Answered
d A d t = 0.5 × A × ( 1 A 100 ) 10
with A ( 0 ) = 70 and we want to use Euler's method to get an approximate value for A ( 10 ), with a step size of 1.
So the answer sheet says you basically have to use Ans + 0.5 × Ans × ( 1 Ans 100 ) 10 with the first Ans being 70, and then of course repeat 10 times.
But I'm wondering, doesn't this actually give you d A ( 10 ) d t ? How is this a correct method?
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Answers (2)

Ricky Lamb
Answered 2022-10-01 Author has 7 answers
The Euler method does not give you d A d t . You give it a formula for d A d t , such as the one in your question. Then from any given point, like your start of (0,70) it puts a straight line through the point with slope d A d t of that point. From your expression, d A d t | ( 0 , 70 ) = 0.5 so we step one unit in t at a slope of 0.5, giving the A value of the next point as 70+0.5⋅1=70.5. Now we are at (70.5,1), we calculate d A d t at this point and take another step along the t axis, and so on until we get to t=10
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tonan6e
Answered 2022-10-02 Author has 2 answers
Your formula is wrong. If the differential equation is d A d t = f ( A ) and your step size is h, the formula is A n + 1 = A n + h f ( A n ).So in this case, A n + 0.5 A n ( 1 A n / 100 ) 10.
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