Please Solve this Question using C++99 Version of C plus. Problem 1 (Numerical Differentiation) The altitude (ft) from the sea level and the corresponding time (sec) for a fictitious rocket were measured as follows: Time Altitude 0 400 10 20 9200 30 40 45640 50 87370 60 70 80 90 100 160100 62070 97360 103430 127900 149630 23840 a) Use the skeleton program below. Write a function (CENTRAL) to numerically compute the velocity from the table above using the central difference scheme. Use equation (18) in the lecture note (14-Numerical Differentiation.pdf) at t=100 and use the equation below at t = 0. Make sure that you attach example runs showing the results from the computer. f(x)~ 4 f(x+h) -f(x+2h) -3 f(x) 2 h b) In the same program, write two functions (FORWARD and BACKWARD) to compute the velocity using the forward and backward difference scheme. c) Output your results in a table comparing the velocity using the different schemes for various values of time (t). e.g., Time FD 0 10 BD where FD, BD, and CD are the forward, backward, and central difference schemes, respectively. d) What conclusion (i.e., detailed conclusion) can you draw from this exercise?SKELETON PROGRAM #include void CENTRAL (....) // Central difference { // Your code here } void FORWARD (....) // Forward difference { // Your code here } void BACKWARD (....) // Backward difference { // Your code here } int main() { // Your code here }
Please Solve this Question using C++99 Version of C plus.
Problem 1 (Numerical Differentiation)
The altitude (ft) from the sea level and the corresponding time (sec) for a fictitious rocket were measured as follows:
Time
Altitude
0
400
10
20
9200
30
40
45640
50
87370
60
70
80
90
100
160100
62070
97360
103430
127900
149630
23840
a) Use the skeleton program below. Write a function (CENTRAL) to numerically compute the velocity from the table above using the central difference scheme. Use equation (18) in the lecture note (14-Numerical Differentiation.pdf) at t=100 and use the equation below at t = 0. Make sure that you attach example runs showing the results from the computer.
f(x)~ 4 f(x+h) -f(x+2h) -3 f(x)
2 h
b) In the same program, write two functions (FORWARD and BACKWARD) to compute the velocity using the forward and backward difference scheme.
c) Output your results in a table comparing the velocity using the different schemes for various values of time (t).
e.g.,
Time
FD
0
10
BD
where FD, BD, and CD are the forward, backward, and central difference schemes, respectively.
d) What conclusion (i.e., detailed conclusion) can you draw from this exercise?SKELETON PROGRAM
#include <stdio.h>
void CENTRAL (....) // Central difference
{
// Your code here
}
void FORWARD (....) // Forward difference
{
// Your code here
}
void BACKWARD (....) // Backward difference
{
// Your code here
}
int main()
{
// Your code here
}
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