Write a matlab function, MATLAB Programming

Assignment Help:

There are many approaches to numerically estimating the derivative of the function.  The relationship:

1605_Write a Matlab function.png

 
is called a forward difference, since the estimate of the derivative at the point x is generated from the value of the function at x and the value of the function at x+?x (a point forward from x).  A backward difference formula estimates the derivative at the point x is from the value of the function at x and the value of the function at x-?x (a point backward from x) as follows:

2479_Write a Matlab function1.png

 
A central difference formula uses values of the function on either side of the point x in order to estimate the value of the function at x, as follows:

2074_Write a Matlab function2.png

 
The central difference formula has the advantage that it is more accurate, for a given ?x, than the forward or backward difference formulas.

In this problem, we will use a combination of the above techniques to estimate the derivative of a function from a set of measured data points.  We will use the following algorithm to estimate the derivative of the function: 
 
where fk is the value of the function at the kth data point, k f ′  is the estimate of the derivative of the function at the kth data point, N is the total number of data points, and  x ?  is the spacing between data points.  Note that we are using a forward difference formula for the first data point, a backward difference formula for the last data point, and a central difference formula for all other data points.

25_Write a Matlab function3.png

(a) Write a Matlab function which implements the above algorithm to estimate the derivative of a function described by a set of data points.  Your function should accept two inputs:

  • the first input is an N-element vector containing the measured values of the function (the fks)
  • the second input is the spacing between data points ( x ? )

Your function should return an N-element vector containing the estimated derivative of the function.  The size of the vectors should be determined by your function.  Your function does not need to do any error checking on the inputs.

(b) Write a script file which uses the function you created in part (a) to calculate and plot the derivative of the function  )x sin( )x(f π 2 = , for  1 0 ≤ ≤ x .  Your script file should do the following:

i.  Create data points for f(x) and use your function to estimate its derivative with  x ? =0.1
ii.  Create data points for f(x) and use your function to estimate its derivative with  x ? =0.01
iii.  Calculate the exact value of the derivative of f(x) for 1 0 ≤ ≤ x at increments of  x ? =0.01
iv.  Plot the above three sets of data on a single figure.  Include a legend to indicate which line corresponds to which case, and label the vertical and horizontal axes appropriately.


Related Discussions:- Write a matlab function

Printing - matrices, Printing - matrices: For matrices, the MATLAB unw...

Printing - matrices: For matrices, the MATLAB unwinds the matrix column by column. For illustration, consider the random 2 × 3 matrix as shown below: >> mat = randint(2,3,[

Plot the input and the output of the filter on a single plot, An FIR filter...

An FIR filter has coefficients b = [ 1.0000   -0.6387    1.0214    0.8210   -0.7470    1.0920 ] (a) Find H(z) for the filter and plot its frequency response (magnitude and phase

Mod function, how to reverse the digits of positive number by using mod fun...

how to reverse the digits of positive number by using mod function?

Find and plot the magnitude of the dtft, An FIR filter has coefficients b =...

An FIR filter has coefficients b = [ 1.0000   -0.6387    1.0214    0.8210   -0.7470    1.0920 ] (a) Find H(z) for the filter and plot its frequency response (magnitude and phase

How to start working with simpower, How to Start Working withSimpower: ...

How to Start Working withSimpower: 1. In the Simulink screen, open a new "Model" (File àNewà Model), name it and save it. 2. Expand the SimPowerSystems library, select and

Assignment`, matlab code for The region bounded by the parabola x2 = y and ...

matlab code for The region bounded by the parabola x2 = y and the line y = x in the first quadrant is rotated about the X-axis to generate a solid. Find the volume of the solid.

Steady-state conduction equation, Problem: Consider a trapezoidal piece of...

Problem: Consider a trapezoidal piece of polymer film as shown below. The parallel sides of the trapezoid are insulated and the temperature of the bottom and diagonal sides are f

Generate two waveforms-analog waveform, The purpose of this lab is to intro...

The purpose of this lab is to introduce students to the basic concept of overtones. In order to generate two tones at the same time, you need to generate two waveforms and add them

Expand a matrix, Expand a matrix: To expand a matrix, an individual el...

Expand a matrix: To expand a matrix, an individual element could not be added as that would mean there would no longer be the similar number of values in every row. Though,

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd