differential equation huen plotting problem
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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!!!
采纳的回答
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')
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