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Numerical analysis w/euler's method

  • Thread starter solowa4
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  • #1
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The amount of a uniform distributed radioactive contaminant contained in a closed reactor is measured by its concentration (c) (Becquerel/liter or Bq/L). The contaminant decreases at a decay rate proportional to its concentration; that is

Decay rate(dc/dt)= -kc
Where (dc/dt) is the change in mass, (k) is a constant with units of (day^-1), and (-kc) is the decrease by decay.

a-use euler's method to solve this eq from t=0 to 1 day with k=0.2 day^-1. Employ a step size of Delta t = 0.1 day. The concentration at t=0 is 10 Bq/L.

b-plot the solution on a semilog graph (ie (ln c) versus (t) and determine th slope.

I am at a loss at where to begin or accomplish this.
 

Answers and Replies

  • #2
hotvette
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Welcome to PF!

Well, the first step is understanding how Euler's Method works. What do you know about it?
 
  • #3
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Not much as I just started the class :( That's why it is giving me difficult time
 
  • #4
hotvette
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  • #5
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I have already looked at this and other sources with no help to my problem.
Thanks for your help
 
  • #6
hotvette
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I have already looked at this and other sources with no help to my problem
Sure it does. It explains the methodology:

y(n+1) = y(n) + h*y'(n)
t(n+1) = t(n) + h

For the Wiki example (i.e. y' = y and h = 1)

t(0) = 0, y(0) = 1, y'(0) = y(0) = 1
t(1) = 0 + 1 = 1, y(1) = y(0) + h*y'(0) = 1 + 1*1 = 2, y'(1) = y(1) = 2
t(2) = 1 + 1 = 2, y(2) = y(1) + h*y'(1) = 2 + 1*2 = 4, y'(2) = y(2) = 4
t(3) = 3 + 1 = 3, y(3) = y(2) + h*y'(2) = 4 + 1*4 = 8, y'(3) = y(3) = 8

In your case, you know that t(0) = 0, y(0) = 10, h = 0.1, and y' = -ky with known value for k.
 

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