ode45 with multiple variables

How can l solve the system with multiple variables using ode45? For example l want to solve the following system for variables x1 x2 y1 y2 with respect to time t:

x1'=x2/4 - (5*x1)/16 + (15*y1)/16 - (3*y2)/4 - x1*(x1^2 + y1^2 - 1) - 3*y1*(x1^2 + y1^2)

y1'= (3*x2)/4 - (15*x1)/16 - (5*y1)/16 + y2/4 + 3*x1*(x1^2 + y1^2) - y1*(x1^2 + y1^2 - 1)

x2'=x1/8 - (5*x2)/16 + x3/8 - (3*y1)/8 + (15*y2)/16 - (3*y3)/8 - x2*(x2^2 + y2^2 - 1) - 3*y2*(x2^2 + y2^2)

y2'=(3*x1)/8 - (15*x2)/16 + (3*x3)/8 + y1/8 - (5*y2)/16 + y3/8 + 3*x2*(x2^2 + y2^2) - y2*(x2^2 + y2^2 - 1)

My question is that is there a simple way to repersent the variables x1 y1 x2 y2 when use ode45 to solve the equations in time rather than defining each variable as A(1)=x1,A(2)=y1A(3)=x2,A(4)=y2

Is there a approach that allows me to:

f=@(t,x1,y1,x2,y2) ...............

[t,R]=(f,tspan,initial condition);

So that i will not need to repersent each variable as the elements in the matrix A. Please help me, thank you very much.

Answer 1

[madhan ravi]

Below is the right way to do , but maybe you're looking for matlabFunction()?

Y = zeros(4,1); 
Y(1)=x1
Y(2)=y1
Y(3)=x2
Y(4)=y2

[Penglin Cai]

can l put x1 y1 x2 y2 directly in the ode45 to solve them with respect to time?

[madhan ravi]

No

[Bjorn Gustavsson]

If you definitely want to use the variable x1 y1 x2 y2 in your ODE-function (there are often decent enough reasons for this in terms of readability), you simply do something like this up top in your ODE-function:

function dAdt = yourODEfcn(t,A)
x1 = A(1);
x2 = A(2);
y1 = A(3);
y2 = A(4);
% etc
% Then remaining code here  
end

[madhan ravi]

Thank you Bjorn was thinking to write in that way but somehow messed it up xD.