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Section 2.5
19.
Use the Matlab code given on page 131 of the textbook. Switch around the
f
and
impeuler
functions,
like this:
function [X,Y]=impeuler(x,y,x1,n)
h=(x1x)/n;
X=x;
Y=y;
for i=1:n
k1=f(x,y);
k2=f(x+h,y+h*k1);
k=(k1+k2)/2;
x=x+h;
y=y+h*k;
X=[X;x];
Y=[Y;y];
end
function yp=f(x,y)
yp=x+sqrt(y);
Save this code into the ﬁle
impeuler.m
. To get an I.E. approximation of, for instance,
y
(2) with initial
value
y
(0) = 1 and step size
h
= 0
.
1, type the commands
[X,Y]=impeuler(0,1,2,2/0.1);
Y(end)
at the command line. The result is that
y
(2)
≈
6
.
4083.
23.
Use the same code as in Problem 19, but change the last line to
yp=sin(x)+cos(y)
. To get an I.E.
approximation of, for instance,
y
(1) with initial value
y
(0) = 0 and step size
h
= 0
.
1, type the commands
[X,Y]=impeuler(0,0,1,1/0.1);
Y(end)
at the command line. The result is that
y
(1)
≈
1
.
2297.
Section 2.6
19.
Use the Matlab code given on page 142 of the textbook. Switch around the
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This homework help was uploaded on 01/21/2008 for the course MATH 2930 taught by Professor Terrell,r during the Spring '07 term at Cornell University (Engineering School).
 Spring '07
 TERRELL,R
 Math, matlab

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