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//Eg-13.3
//pg-525
clear
clc
close()
x(1) = 0;
yb(1) = 0;
y(1) = 1; //Initial condition
h = 0.1;
deff('out = func(in1,in2)','out = in1^2*in2')
//Taking the exact values from the previous problem
z(1) = exp(x(1)^3/3);
for(i = 2:11)
x(i) = 0.1+(i-2)*0.1;
z(i+1) = exp(x(i)^3/3);
end
for(i = 1:10)
yb(i+1) = y(i) + h*func(x(i),y(i));
y(i+1) = y(i) + h/2*(func(x(i),y(i)) + func(x(i+1),yb(i+1)));
end
printf(' x yPc yExact\n')
for(i = 2:11)
printf('%f %f %f\n',x(i),y(i),z(i+1))
end
for(k = 1:10)
a(k) = x(k+1);
b(k) = y(k+1);
c(k) = z(k+2);
end
clf()
//plot(a,[b c])
plot(a,b,'-')
plot(a,c,'.')
legend('Exact','Euler')
xlabel('x')
ylabel('y')
printf('\n\nA comparison of Eulers method, the predictor-corrector method, and the exact solution\nare presented in the image. As expected, the predictor-corrector method produces a more\naccurate solution than the simple Eulers method.\n')
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