## Help: numerical solution for first order differential (OD) equations

### Dushyant (view profile)

on 15 Sep 2013

I need some guidance regarding numerical ordinary differential equation

I have nine simultaneous first order differential (OD) equations which can be combinedly written as: dY/dt = A*Y + b where Y is a vector consisting of 9 terms and A is a matrix of size 9,3.

Can someone suggest me how should I start?

The paper that, I am looking at, briefly explains the procedure as: “The problem can be analytically without further simplification with the use of Matlab built-in function of matrix left division (\) and matrix power (expm 1) “ Regards, DK

Azzi Abdelmalek

### Azzi Abdelmalek (view profile)

on 15 Sep 2013

If Y is 9x1 array and A is 9x3 array, how can you do A*Y ?

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### Azzi Abdelmalek (view profile)

on 15 Sep 2013
```A should be a 9x9 array
```

write and save this function as myeq.m

```function dY=myeq(t,Y)
A=randi(9,9,9) ; % Example
b=1;
dY=zeros(9,1)   ;
dY = A*Y + b;
```

Then call it

```y0=zeros(9,1)% Initial conditions
tspan=[0 10];
[t,y]=ode45(@myeq2,tspan,y0)
```

Azzi Abdelmalek

### Azzi Abdelmalek (view profile)

on 16 Sep 2013

[ Dushyant commented]

Thanks.

Sorry, I mistakenly wrote wrong dimension for A.

Regards, Dushyant