Use the Secant method with initial guesses of and
to calculate the root/s of the equation
up to three iterations. Calculate the absolute relative approximate error at each stage.
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What would be the maximum possible period of this random number sequence?
What are the advantages and drawbacks of the Secant method when compared to the Bisection Method and the Newton-Raphson Method?
Explain round-off error and truncation error, with one example of each.
A population of single-celled organisms was grown in a Petri dish over a period of 24 hours. The number of organisms at a given time is recorded in the table below. Fit the data in the table below to an exponential model :
| x (time in hours) | 0 | 4 | 8 | 12 | 16 | 20 | 24 |
| y | 25 | 36 | 52 | 68 | 85 | 104 | 142 |
Derive the Runge-Kutta 2nd Order formula for the differential equation
Derive the Runge-Kutta 2nd Order formula for the differential equation
Use this to determine the value of y at given that
, using a step size
.
The series for ex can be written as:
Calculate the truncation error when the first four terms of the series are used to evaluate e1.5.