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//Eg-13.15
//pg-559
clear
clc
deff('out = func(in1,in2)','out = 0.5*(1+in1)*in2^2')
x(1) = 0;
y(1) = 1;
h = 0.001;
n = 0.3/0.001;
for(i = 1:n)
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;
for(i = 1:n)
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(' t y F(t,y)\n')
for(i = 0:3)
printf('%f %f %f\n',x(i*100+1),y(i*100+1),func(x(i*100+1),y(i*100+1)))
end
//Using equations [61] and [62]
y0 = y(1);
y1 = y(101);
y2 = y(201);
y3 = y(301);
x0 = x(1);
x1 = x(101);
x2 = x(201);
x3 = x(301);
x4 = 0.4;
h = 0.1;
y4b = y0 + 4*h/3*(2*func(x3,y3) - func(x2,y2) + 2*func(x1,y1));
y4 = y2 + h/3*(func(x2,y2) + 4*func(x3,y3) + func(x4,y4b));
printf('\nThe value of y4 = %f\n',y4)
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