The following is a Matlab program (second version)
to solve differential equations
numerically using
Euler's Method .
This variation will give the graph/solution on two sides of
the innitial-time.
I will explain how to use it at the end:
The Program:
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function y=y(n,t0,t1,y0)
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h=(t1-t0)/n;
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t(1)=t0;
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y(1)=y0;
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for i=1:n
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t(i+1)=t(i)+h;
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y(i+1)=y(i)+h*ex(t(i),y(i));
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end;
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t(n+1)=t0;
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y(n+1)=y0;
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for i=n+1:2*n
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t(i+1)=t(i)-h;
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y(i+1)=y(i)-h*ex(t(i),y(i));
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end;
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for i=1:n
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T(i)=t(2*n-i+1);
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Y(i)=y(2*n-i+1);
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end;
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for i=n+1:2*n
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T(i)=t(i-n);
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Y(i)=y(i-n);
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end;
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V=[T',Y']
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plot(T,Y)
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title('satya')
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How to Use the Program?
- You have to have the above program in a
filename.m-file. I would call it
eulertwo.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:
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%x is a function of t and y is the first derivative x'(t)
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function y=y(t,x)
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y=(t^2-x^2)*sin (x);
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- Now, on matlab prompt, you write
eulertwo(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.