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//Eg-13.16
//pg-562
clear
clc
deff('out = func(in1,in2)','out = sin(in1)-in2')
//To get the answers in the text book we shouldn't take sint=Vs to be unity!
x(1) = 0;
y(1) = 0;
h = 0.1;
for(i = 1:10)
x(i+1) = x(i) + h;
end
a = (2^0.5-1)/2;
b = (2-2^0.5)/2;
c = -(2^0.5)/2;
d = 1 + (2^0.5)/2;
printf(' t y\n')
for(i = 1:4)
k1(i) = h*func(x(i),y(i));
k2(i) = h*func(x(i)+h/2,y(i)+k1(i)/2);
k3(i) = h*func(x(i)+h/2,y(i)+a*k1(i)+b*k2(i));
k4(i) = h*func(x(i)+h,y(i)+c*k2(i)+d*k3(i));
y(i+1) = y(i) + 1/6*(k1(i)+2*b*k2(i)+2*d*k3(i)+k4(i));
printf('%f %f\n',x(i),y(i))
end
h = 0.1;
for(i = 4:10)
yb(i+1) = y(i-3) + 4*h/3*(2*func(x(i-1),y(i-1)) + 2*func(x(i-2),y(i-2)));
y(i+1) = y(i-1) + h/3*(func(x(i-1),y(i-1)) + 4*func(x(i),y(i)) + func(x(i+1),yb(i+1)) );
end
printf('\n\nUsing the Milnes predictor-corrector Method:\n\n')
printf(' t y\n')
for(i = 5:11)
printf('%f %f\n',x(i),y(i))
end
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