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//Eg-13.11
//pg-550
clear
clc
deff('out = func(in1,in2)','out = -2*in2')
for(j = 1:3)
x(1) = 0;
y(1,j) = 1;
yb(1,j) = 0;
end
h(1) = 0.43;
h(2) = 0.3;
h(3) = 0.03;
z(1) = exp(-2*x(1));
for(i = 2:11)
x(i) = 0.1+(i-2)*0.1;
z(i+1) = exp(-2*x(i));
end
for(j = 1:3)
for(i = 1:10)
yb(i+1,j) = y(i) + h(j)*func(x(i),y(i,j));
y(i+1,j) = y(i) + h(j)/2*(func(x(i),y(i,j)) + func(x(i+1),yb(i+1,j)));
end
end
printf(' x h1 h2 h3 exact\n')
for(i = 2:11)
printf('%f %f %f %f %f\n',x(i),y(i,1),y(i,2),y(i,3),z(i+1))
end
for(i = 1:10)
a(i) = x(i+1);
b(i) = y(i+1,1);
c(i) = y(i+1,2);
d(i) = y(i+1,3);
e(i) = z(i+2);
end
clf()
//plot(a,[b c d e])
plot(a,b,'s')
plot(a,c,'o')
plot(a,d,'d')
plot(a,e,'-')
legend('h = 0.43','h = 0.3','h = 0.03','analytical')
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