DGM（2,1）模型

clc,clear;
x0=[2.874 3.278 3.39 3.679 3.77 3.8];
n=length(x0);
a_x0=diff(x0)';
B=[-x0(2:end)',ones(n-1,1)];
u=B\a_x0

syms x(t)
d2x=diff(x,2);dx=diff(x);

x=dsolve(d2x+u(1)*dx==u(2),x(0)==x0(1),dx(0)==x0(1));
xt=vpa(x,6)
yuce=subs(x,t,[0:n-1]);
yuce=double(yuce)
x0_hat=[yuce(1),diff(yuce)]
epsilon=x0-x0_hat;
delta=abs(epsilon./x0)

result

u =

    0.424
   1.7046

xt =

4.0202t + 2.70331exp(-0.423997*t) + 0.170692

yuce =

    2.874         5.96       9.3688       12.989       16.747       20.596

x0_hat =

    2.874        3.086       3.4088       3.6201       3.7584       3.8488

delta =

        0     0.058572     0.005556     0.016008    0.0030859     0.012855