solving the differential equation

I want to solve the below equations. In these equations Q,Tp are variables, and italic underlined alphabets are constant. Also, Irr and Te are matrices with one row and 18 columns. I want to obtain Q and Tp as matrices with one row and 18 columns according to the amount of Irr and Te. My question is 'how can I solve these equations'?

dQ/dt=A * Irr * Tp + B * Te * Tp

if Q<C

Tp=D* Q

if E<Q<F

Tp=H

if Q>G

Tp=M* Q

[Torsten]

As already answered in a previous question, use ode45 or ode15s to solve for Q1,Q2,...Q18.

Answer 1

[Walter Roberson]

Your system cannot work.

dQ/dt=A * Irr * Tp + B * Te * Tp

You say that Irr and Te are matrices with one row and 18 columns. If, hypothetically, Tp was scalar, then dQ/dt would be the sum of two expressions that were each 1 x 18 and the result would be 1 x 18, which would be (locally) self-consistent so far.

Then you reach the if and you see the first branch and last branch assign Tp = constant times Q. But Q is 1 x 18, so Tp would have to be 1 x 18, contradicting the assumption that Tp is scalar.

So we have to go back to

dQ/dt=A * Irr * Tp + B * Te * Tp

this time with the assumption that irr and Te and Tp are each 1 x 18. But you have Irr * Tp and that is a (1 x 18) * a (1 x 18). Which is an invalid operation, inner product between two row vectors.

You cannot get the correct sizes out unless you use element-by-element multiplication, .* instead of inner product, *

[Torsten]

For Q, Tp, Irr and Te being 1x18 and elementwise multiplication in

dQ/dt=A * Irr .* Tp + B * Te .* Tp

the if-statement could be interpreted elementwise:

if Q(i)<C

Tp(i)=D* Q(i)

if E<Q(i)<F

Tp(i)=H

if Q(i)>G

Tp(i)=M* Q(i)

(1<=i<=18)

At least this is the only interpretation that makes sense.

[Walter Roberson]

In later postings the dQ expressio got revised to not have the multiplication by Tp .