Simple Commands in MATLAB

Functions

x=0:0.001:1; Enter the range of x values.

y=4.*x.*(1-x); Enter the function. Note the .* for multiplying elements of the matrix.

 

2D Plots

plot(x,y)

To plot two graphs, we define the function(s). For composite functions it would be better to define a function in a file called map1d.m, with the following lines:

function y=map1d(x)

y=4.*x.*(1-x);

Now plot using plot command.

plot(x,map1d(map1d(x)),x,x)

 

Iteration

To carry out the iteration, one should create a new m-file and save it. One then needs to specify the initial value and loop through the iteration process with a for loop as shown below.

Create a file called iter1d.m with the following lines:

x(1)=0.40; (Starting value – index starts at 1)

for n=2:100 (loop)

x(n)=map1d(x(n-1)); (apply function)

end (end loop)

First clear all of the variables used so far:

clear

In Matlab, type

iter1d

 

Displaying Results

map1d(.2)

ans =

0.6400

x(1:10)

ans =

Columns 1 through 7

0.4000 0.9600 0.1536 0.5200 0.9984 0.0064 0.0255

Columns 8 through 10

0.0993 0.3577 0.9190

plot(x)

 

Finding Roots –

Fixed point equation: Create a function file map1dP2 to solve g(x)=0 for g(x)=f(f(x))-x and f(x)=2.1*x*(1-x).

function y=map1dP2(x)

z=2.1.*x.*(1-x);

y=2.1.*z.*(1-z)-x;

fzero('map1dP2',.7)

Zero found in the interval: [0.476, 0.85839].

ans =

0.5238