MATLAB：微分方程（组）数值解

一、显式微分方程

clc,clear
tspan = [0:10]; 
y0 = 2;
[t1,y1] = ode23(@odefun_1,tspan,y0); %求数值解，精度相对低
[t2,y2] = ode113(@odefun_1,tspan,y0); %求数值解，精度相对高
yt = sqrt(tspan'+1)+1; %求精确解
subplot(1,2,1)
plot(t1,y1,'bo',t2,y2,'r*',tspan,yt,'g-')
legend('ode23求解','ode113求解','精确解','Location','best');
subplot(1,2,2)
y1t = abs(y1-yt); 
y2t = abs(y2-yt);
plot(t1,y1t,'bo',t2,y2t,'r*')
legend('ode23误差','ode113误差','Location','best');

function dydt = odefun_2(t,y)
    ft = 2*sin(t).*(t=4*pi); %定义分段函数f(t)
    gt = cos(t).*(t>=3.5*pi) + 0.*(t