Explain why a polynomial is a useful choice for an interpolating function.
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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
.
What are the advantages and drawbacks of the Secant method when compared to the Bisection Method and the Newton-Raphson Method?
Use the LU decomposition method to solve the following system of equations:
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.
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 |
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.
What would be the maximum possible period of this random number sequence?