differential equation huen plotting problem

 x_a=linspace(0,2,n)
     h=x_a(n)-x_a(n-1)
     y_a=((x_a.^2+1/2.*x_a+1)).^2 
     for i=1:n-1 ;
    
     x_h=linspace(0,2,n)
     h_h=x_h(n)-x_h(n-1)
     A(i)=x_h(i)+h_h
     B(i)=y_h(i)+h_h*(1+4.*x_h(i)).*sqrt(y_h(i))
     L(i)=(1+4.*x_h(i)).*sqrt(y_h(i))
     R(i)=(1+4.*A(i)).*sqrt(B(i))
      y_h(1)=1;
     y_h(i+1)=y_h(i)+1/2.*(h_h.*L(i).*R(i))
     i=i+1;
     end
     plot(x_a,y_a,'--kd')
     hold on
     plot(x_h,y_h,'--rx')

Above code is to comapre the value of diffrenetial equation by analytic method and huen method by plotting it on graph.

But,Dont know why its not plotting the graph correctly.

If I am plotting the analytic solution graph individually its plotting the correct graph.But when I am plotting the two graphs together,none of the two graphs are correct.

Please help!!!

Answer 1

[Walter Roberson]

You did not initialize y_h(1) before you used it.

Your plots are very different scales: your analytic goes up to about 40 but your heun goes to about 10^10 .

This suggests that you have programmed your heun incorrectly.

format long g
n = 127;
x = linspace(0,2,n);
h = x(n)-x(n-1);
y_a =((x.^2+1/2.*x+1)).^2;
y_h(1) = 1;
for i=1:n-1
 A(i) = x(i) + h;
 B(i) = y_h(i) +h*(1+4.*x(i)).*sqrt(y_h(i));
 L(i) = (1+4.*x(i)).*sqrt(y_h(i));
 R(i) = (1+4.*A(i)).*sqrt(B(i));
 y_h(i+1) = y_h(i) + 1/2.*(h.*L(i).*R(i));
end
plot(x,y_a,'--kd')

 figure
 plot(x,y_h,'--rx')