用四阶龙格库塔法求解矩阵微分方程要求电流就是求解矩阵微分方程：（R+pM(t)）*I(t)+M(t)*pI(t)-U(t)=0,其中p是求导,R是6*6常数矩阵,M(t)是6*6的时变矩阵,U(t)是6*1的时变矩阵,求I(t),也是6*1的矩阵.已

用四阶龙格库塔法求解矩阵微分方程要求电流就是求解矩阵微分方程：（R+pM(t)）*I(t)+M(t)*pI(t)-U(t)=0,其中p是求导,R是6*6常数矩阵,M(t)是6*6的时变矩阵,U(t)是6*1的时变矩阵,求I(t),也是6*1的矩阵.已
用四阶龙格库塔法求解矩阵微分方程
要求电流就是求解矩阵微分方程：（R+pM(t)）*I(t)+M(t)*pI(t)-U(t)=0,
其中p是求导,
R是6*6常数矩阵,
M(t)是6*6的时变矩阵,
U(t)是6*1的时变矩阵,
求I(t),也是6*1的矩阵.
已知条件：
M=[ 0,0,0,-15727/10000*sin(5/12*pi+80*pi*t)*pi,15727/10000*cos(1/4*pi+80*pi*t)*pi,15727/10000*sin(1/12*pi+80*pi*t)*pi;
0,0,0,15727/10000*sin(1/12*pi+80*pi*t)*pi,-15727/10000*sin(5/12*pi+80*pi*t)*pi,15727/10000*cos(1/4*pi+80*pi*t)*pi;
0,0,0,15727/10000*cos(1/4*pi+80*pi*t)*pi,15727/10000*sin(1/12*pi+80*pi*t)*pi,-15727/10000*sin(5/12*pi+80*pi*t)*pi;
-15727/10000*sin(5/12*pi+80*pi*t),15727/10000*sin(1/12*pi+80*pi*t)*pi,15727/10000*cos(1/4*pi+80*pi*t)*pi,0,0,0;
15727/10000*cos(1/4*pi+80*pi*t)*pi,-15727/10000*sin(5/12*pi+80*pi*t)*pi,15727/10000*sin(1/12*pi+80*pi*t)*pi,0,0,0;
15727/10000*sin(1/12*pi+80*pi*t)*pi,15727/10000*cos(1/4*pi+80*pi*t)*pi,-15727/10000*sin(5/12*pi+80*pi*t)*pi,0,0,0];
U=[380*cos(100*pi*t);
380*cos(100*pi*t-2*pi/3);
380*cos(100*pi*t+2*pi/3);
0;
0;
0];
R=[0.0247,0,0,0,0,0;
0,0.0247,0,0,0,0;
0,0,0.0247,0,0,0;
0,0,0,0.0193,-0.0193,0;
0,0,0,0,0.0193,-0.0193;
0,0,0,1,1,1];
电流I的初值是：I(0)=[0;0;0;0;0;0];
t是时间
预期最后的结果是6个电流与时间的关系

用四阶龙格库塔法求解矩阵微分方程要求电流就是求解矩阵微分方程：（R+pM(t)）*I(t)+M(t)*pI(t)-U(t)=0,其中p是求导,R是6*6常数矩阵,M(t)是6*6的时变矩阵,U(t)是6*1的时变矩阵,求I(t),也是6*1的矩阵.已
global R M U
syms t
R=[
0.0247,0,0,0,0,0;
0,0.0247,0,0,0,0;
0,0,0.0247,0,0,0;
0,0,0,0.0193,-0.0193,0;
0,0,0,0,0.0193,-0.0193;
0,0,0,1,1,1
];
M=[
0,0,0,-15727/10000*sin(5/12*pi+80*pi*t)*pi,15727/10000*cos(1/4*pi+80*pi*t)*pi,15727/10000*sin(1/12*pi+80*pi*t)*pi;
0,0,0,15727/10000*sin(1/12*pi+80*pi*t)*pi,-15727/10000*sin(5/12*pi+80*pi*t)*pi,15727/10000*cos(1/4*pi+80*pi*t)*pi;
0,0,0,15727/10000*cos(1/4*pi+80*pi*t)*pi,15727/10000*sin(1/12*pi+80*pi*t)*pi,-15727/10000*sin(5/12*pi+80*pi*t)*pi;
-15727/10000*sin(5/12*pi+80*pi*t),15727/10000*sin(1/12*pi+80*pi*t)*pi,15727/10000*cos(1/4*pi+80*pi*t)*pi,0,0,0;
15727/10000*cos(1/4*pi+80*pi*t)*pi,-15727/10000*sin(5/12*pi+80*pi*t)*pi,15727/10000*sin(1/12*pi+80*pi*t)*pi,0,0,0;
15727/10000*sin(1/12*pi+80*pi*t)*pi,15727/10000*cos(1/4*pi+80*pi*t)*pi,-15727/10000*sin(5/12*pi+80*pi*t)*pi,0,0,0
];
U=[
380*cos(100*pi*t);
380*cos(100*pi*t-2*pi/3);
380*cos(100*pi*t+2*pi/3);
0;
0;
0
];
DM=diff(M,t);
%%%要调节的参数在这里
%%注意,你的M有点奇异,计算很快发散掉了,你检察一下相关的参数吧.
%%det(subs(M,t,0))
I0=[0;0;0;0;0;0];
tstart=0;
tend=0.1;
dt=0.1;
%%%end
tout=tstart:dt:tend;
n=length(tout);
M_t_dt=subs(M,t,tstart);
U_t_dt=subs(U,t,tstart);
DM_t_dt=subs(DM,t,tstart);
II=I0;
for i=1:n-1
tt=tout(i);
M_t=M_t_dt;
U_t=U_t_dt;
DM_t=DM_t_dt;
M_t_dt_2=subs(M,t,tt+dt/2);
U_t_dt_2=subs(U,t,tt+dt/2);
DM_t_dt_2=subs(DM,t,tt+dt/2);
M_t_dt=subs(M,t,tt+dt);
U_t_dt=subs(U,t,tt+dt);
DM_t_dt=subs(DM,t,tt+dt);
k1=dt*M_t \(U_t -(R+DM_t )*(II(:,end) ));
k2=dt*M_t_dt_2\(U_t_dt_2-(R+DM_t_dt_2)*(II(:,end)+0.5*k1));
k3=dt*M_t_dt_2\(U_t_dt_2-(R+DM_t_dt_2)*(II(:,end)+0.5*k2));
k4=dt*M_t_dt \(U_t_dt -(R+DM_t_dt )*(II(:,end)+k3 ));
I_t=II(:,end)+(k1+2*k2+2*k3+k4)/6;
II=[II,I_t];
end
plot(tout',II')