The approximate value of the derivative of a function f(x)at x can be calculated using the
formula:
Calculate for
and (ii) h = 0.05.
Determine the true error and relative true error in each case.
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Use the bisection method in the interval [2,4] to calculate the root/s of the equation
up to three iterations. Calculate the absolute relative approximate error at each stage.
se Euler’s method for the differential equation with the initial condition y(0) = 2 to calculate y(2) . Take a value of step size h = 0.5 .
What are the advantages and drawbacks of the bisection method?
Use the Gauss elimination method to solve the system of equations:
x1 - 2x2 + x3 = 0 ; 2x1 + x2 - 3x3 = 5 ; 4x1 -7x2 + x3 = -1
In what way is the Newton-Raphson method more beneficial than the bisection method?
Given the following data for the velocity as a function of time, calculate the velocity at t = 12 s using second order polynomial interpolation in the Newton divided difference method:
| Time (in s) | 0 | 15 | 18 | 22 | 24 |
| Velocity (in ms-1) | 20 | 25 | 35 | 30 | 80 |
The approximate value of the derivative of a function f(x)at x can be calculated using the
formula:
Calculate for
and (ii) h = 0.05.
Determine the true error and relative true error in each case.