Solving System of Differential Equations with Multiple Variables using ode45
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Lets say I have a system of six differential equations with multiple variables:
dA = E - C + B - D
dB = F - D + A - C
.....
dF = - B + D - F
How can I write a function which is solvable with ode45? I want a 1x6 initial condition input and a 1x6 output over a time span.
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Star Strider
2020-6-24
If you assign ‘A(t)’ as ‘x(1)’ ... ‘F(t)’ as ‘x(6)’, then an anonymous function version would create this matrix:
dfcn = @(t,x) [x(5) - x(3) + x(2) + x(4)
x(6) - x(4) + x(1) - x(3)
. . .
-x(2) + x(4) + x(6)];
and then call ode45 with ‘dfcn’ and the appropriate initial conditions and time span.
The function gets a bit more complicated if involves derivatives of the functions on the right hand side. For that, I usually use the Symbolic Math Toolbox to create the equations, then odeToVectorField to create them as first-order equations, and matlabFunction to convert them to a system that ode45 can use. (Sure, I could do them by hand and then spend a bit of time sorting my algebra errors, but there is no reason to do that.)
2 个评论
Anna Jacobsen
2021-2-9
This looks like a great solution! I am trying to solve a similar problem. Could you clarify what you mean by assigning A(t) to x(1)? Would A(t) be the differential equation dA/dt?
Star Strider
2021-2-9
Anna Jacobsen — Thank you!
‘Could you clarify what you mean by assigning A(t) to x(1)?’
Here 
is the first equation, ao ‘A(t)’ gets assigned as ‘x(1)’, with the other variables assigned in order, so ‘B(t)’ is ‘x(2)’ and similarly for the others.
is the first equation, ao ‘A(t)’ gets assigned as ‘x(1)’, with the other variables assigned in order, so ‘B(t)’ is ‘x(2)’ and similarly for the others. ‘Would A(t) be the differential equation dA/dt?’
The derivatives are implicitly on the left-hand-side of the equation, so if this were not an anonymous function (and instead a function file), the code for 
would be:
would be: dxdt(:,1) = x(5) - x(3) + x(2) + x(4);
and similarly for the others.
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