Differential Equations : Euler Method : Matlab Program

Satyagopal Mandal

Department of Mathematics

University of Kansas

Office: 624 Snow Hall Phone: 785-864-5180

e-mail: mandal@math.ukans.edu

© Copy right Laws Apply. My Students have the permission to copy.

The following is a Matlab program to solve differential equations numerically using Euler's Method . I will explain how to use it at the end:

%function t=t(n,t0,t1,y0)

function y=y(n,t0,t1,y0)

h=(t1-t0)/n;

t(1)=t0;

y(1)=y0;

for i=1:n

t(i+1)=t(i)+h;

y(i+1)=y(i)+h*ex(t(i),y(i));

end;

V=[t',y']

plot(t,y)

title('satya')

You have to have the above program in a filename.m-file. I would call it euler.m.
You also have to have a file ex.m and you type in your equation in the file. I typed in a problem as follows:

%x is a function of t and y is the first derivative x'(t)
function y=y(t,x)

y=(t^2-x^2)*sin (x);
Now, on matlab prompt, you write euler(n,t0,t1,y0) and return , where n is the number of t-values, t0 and t1 are the left and right end points and y(t0)=y0 is the innitial condition.
Matlab will return your answer. You should also get the graph, if your computer is set up properly. I do not get the graph in my office but I get it in the lab.