Problem number 761351376

Numerical Integration using Euler's Method

IV Bolus - Linear One Compartment

Your challenge is to use Euler's method to integrate a simple differential equation. The differential equation for drug amount in the body after a single IV bolus dose is described by:

dX/dt = -kel * X

Using an initial amount (dose) of 100 mg calculate the amount remaining after 6 steps of 0.025 hr, (i.e. a total of 0.15 hr). Use an elimination rate constant of 0.173 hr^-1 for this calculation. Instead of using the Laplace transform method to integrate the equation analytically you can use Euler's method to solve the problem numerically. Calculate the amount remaining at the end of each step using the equation:

X_new = X_old + slope * StepSize

where

slope = dX/dt = -kel * X

Time (hr) Slope (mg/hr) Δ Amount (mg) Amount (mg)

0
100

0.025

0.05

0.075

0.1

0.125

0.15

Compare the amount remaining at 0.15 hr with the 'exact' answer you get using the integrated equation:

Amount Remaining = 100 x e^{-0.173 x 0.15} =

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Last update: Tue 27 Dec 2005 02:39:50 pm

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Time (hr)	Slope (mg/hr)	Δ Amount (mg)	Amount (mg)
0			100
0.025
0.05
0.075
0.1
0.125
0.15