Solving Matrix Differential Equations with ODE45

[madjid222]

If we have differential variable of matrix kind ( with dimention 3*3 ) and non matrix ( with dimention 1) simaltanously and as a couple ,how can we use ode45 ?
If we have only matrix kind , we can use m file of ode at first with the command of reshape (3,3) and then change it to column one.What is the solution in this case ?
P,Q,Q :matrices 3*3
Pdot= A*P +P*A’ +Q
K=P*[1 0 0]
xdot(1) =f(x(1),x(2),x(3)) +k(1)*x(1)
xdot(2)=g(x(1),x(2),x(3)) +k(2)*x(2)
xdot(3)=h(x(1) ,x(2),x(3)) +k(3)*x(3)
x0=[ xa;xb;xc]
P0=x01

Example (only matrix differential equation) :
%-----MAIN M-FILE--------------
clear all
%-----VARIABLE SET-UP--------------

A = [0 1 0; 0 0 5; 1 2 3];
Q = [1 0 0; 0 0.5 0; 0 0 0.9];
%-----TO RUN and PLOT ODE SOLUTION--------------
t01= 0;
tf1=30;
tspan1 = LINSPACE(t01, tf1);
X01=zeros(3);
[Time1,X1] = ode45(@(t,X) odefuncare(t,X,A,Q),tspan1,X01);
plot(Time1,X1)
%-------ODEFUNCTION------------------
function dxdt = odefuncare(t,X,A,Q)
X = reshape(X,3,3); %converting X from a column vector generated by ode45 into a 5 x 5 Matrix
dxdt=A*x +x*A’ +Q
dxdt = dxdt(:); %converting dxdt into a column vector as expected by ode45

 

[Valkarie]

endExample (differential equation with matrix and non matrix variables) :%-----MAIN M-FILE--------------clear all%-----VARIABLE SET-UP--------------A = [0 1 0; 0 0 5; 1 2 3];Q = [1 0 0; 0 0.5 0; 0 0 0.9];%-----TO RUN and PLOT ODE SOLUTION--------------t02= 0;tf2=30; tspan2 = LINSPACE(t02, tf2); X02=[zeros(3);0];[Time2,X2] = ode45(@(t,X) odefuncb(t,X,A,Q),tspan2,X02);plot(Time2,X2)%-------ODEFUNCTION------------------function dxdt = odefuncb(t,X,A,Q) X1 = X(1:3,1); % First 3 elements of X vectorX2 = X(4,1); % 4th element of X vectorX1 = reshape(X1,3,3); %converting X1 from a row vector generated by ode45 into a 3 x 3 Matrixdxdt1=A*x1 +x1*A’ +Q;dxdt2=f(X1,X2);dxdt=[dxdt1(:);dxdt2]; %converting dxdt into a column vector as expected by ode45end