Question

The amount of a uniformly distributed radioactive contaminant contained in a closed reactor is measured by its concentration c (Becquerel/litre or Bq/L). The contaminant decreases at a decay rate proportional to its concentration; that is decay ratekc, where k is a constant with units of day1. Given that k- 0.175day1, determine the contaminant concentrations from t-0 to t-5 days with a step size of 0.1 days using: A. Euler's methoo B. Heun's methood C. Midpoint method D. MATLAB's ode45 Assume the concentration at t-0 is 100 Bq/L. Plot the solutions of all parts in a single figure and print out the concentration value at t=5 days for all parts.

Please answer the question in MATLAB coding.

Answer 1

In order to use Euler's Method we first need to rewrite the differential equation into the fom given in From this we can see that Also note that t,0 and yo1. We can now start doing some computatons -4(0 So, the approximation to the solution at t, = 0.1 isy, At the next step we have 0.9 e4-2(0.9)--0.470320046 -4(0.1 ) _ 2(0.9)--O 470320046 Λ = /( 0.1,0.9)-2-e y,-M + hJ-0.94(0.1)(-0.470320046)-0.852967995 -(0.1,0.9)-2-2(0.9) -0470320046 ½ = M +#A = 0.9 +(0. 1) (-0.470320046) = 0.852967995 In order to use Euler's Method we first need to rewrite the differential equation into the fom given in From this we can see that Also note that to 0 and yo-1. We can now start doing some computations -4(0) fo(0.1)-2-e-2(1)1 So, the approximation to the solution at t-0.1 isy, 0.9