Exploring Octave/Matlab Code for Series Evaluation and Function Plotting

Question:

(a) Write an Octave/Matlab code to evaluate the following series Lu-, in which ,, is not known explicitly (10) but is given in terms of a recurrence relation Un+1 = (un-1)2 + (n.)? 2 with u = 0.5 and ug = 0.6. You should stop the summation when ur] < 10-8

(b) For a given Octave code below for plotting a function/s. Explain in detail the consequences of each (7 coding statement for our plot.

Answer:

Series Evaluation Code:

For evaluating the series Lu-, we can use the following Octave/Matlab code based on the given recurrence relation:

u = 0.5;
ug = 0.6;
n = 1;
un = u;
while abs(u) >= 1e-8
  u = un^2 + n^2;
  un = u;
  n = n + 1;
end
disp(u);
        

This code initializes the variables u, ug, n, and un, then iteratively calculates the next term in the series using the recurrence relation Un+1 = (un-1)^2 + n^2 until the absolute value of the term becomes less than 1e-8. Finally, the code displays the evaluated value of the series.

Function Plotting Code Consequences:

The given Octave code creates a 2x2 grid of subplots and plots the function defined by the z values in each subplot. Here is a detailed explanation of the consequences of each coding statement:

1. (x, y) = meshgrid(-3:0.3:3);: This statement creates a grid of x and y values using the meshgrid function. It generates x values from -3 to 3 with a step size of 0.3.
2. z = x .* exp(-x.^2 - y.^2);: This statement calculates the values of the function z using the x and y values with element-wise multiplication and exponential calculation.
3. subplot(2,2,1) mesh(z), title(subplot(2,2,1));: This statement creates the first subplot in a 2x2 grid and plots the surface defined by z values. It also sets the title for the subplot.
4. subplot(2,2,2) mesh(z) view(-37.5,70), title(subplot(2,2,2));: This statement creates the second subplot, changes the viewing angle, and sets the title for the subplot.
5. subplot(2,2,3) mesh(z) view(37.5,-10), title(subplot(2,2,3));: This statement creates the third subplot, changes the viewing angle, and sets the title for the subplot.
6. subplot(2,2,4) mesh(z) view(0,0), title(subplot(2,2,4));: This statement creates the fourth subplot, changes the viewing angle, and sets the title for the subplot.