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//Eg-13.7
//pg-537
clear
clc
A = 0.9;
B = 0.09;
y(1) = 1;
deff('out = func(in1,in2)','out = A*in2 - B*in2^2')
h = 0.5;
//Given the expression of analytical solution : y(t) = 10/(1+9*exp(-0.9*t))
//The index again is 1-11 instead of 0-10
for(i = 1:11)
x(i) = 0 + (i-1)*h;
yex(i) = 10/(1+9*exp(-0.9*x(i)))
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(' x yRKG yExact\n')
for(i = 1:10)
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 %f\n',x(i+1),y(i+1),yex(i+1))
end
printf('\nTherefore, it is observed that the RKG solution closely matches \nwith the analytical solution.\n')
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