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//Eg-13.13
//pg-554
clear
clc
y(1) = 1;
deff('out = func(in1,in2)','out = 1-in1+4*in2')
h = 0.1;
//The index again is 1-11 instead of 0-10
for(i = 1:11)
x(i) = 0 + (i-1)*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;
for(i = 1)
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));
end
printf('The solution is summarized as :\n')
printf(' x y\n')
for(i = 1:2)
printf('%f %f\n',x(i),y(i))
end
//we take x(1) = 0 and x(2) = 0.1, y(1) = 1 and y(2) = 1.608933
h = 0.1;
for(i = 3:5)
yb(i) = y(i-2) + 2*0.1*func(x(i-1),y(i-1));
y(i) = y(i-1) + 0.1/2*(func(x(i-1),y(i-1)) + func(x(i),yb(i)))
printf('%f %f\n',x(i),y(i))
end
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