I have a set of 3 differential equation:
$\begin{cases}\dfrac{dy_1}{dt}=s(y_2+y_1-y_1y_2-qy_1^2)\\\dfrac{dy_2}{dt}=\dfrac{1}{s}(-y_2+y_3-y_1y_2)\\\dfrac{dy_3}{dt}=w(y_1-y_3)\end{cases}$
where $s=77.27$ , $w=0.161$ , $q=8.375\times10^{-6}$
Initial condition: $y_1(0)=4$ , $y_2(0)=1.1$ and $y_3(0)=4$
I want to solve above equation for interval $t=[0,1500]$
The set is stiff and I want to solve it by gear method.
I want to write a Matlab code for solving above equation and I don't have permission to use ready functions of Matlab for example ode15s or other functions.
But my question is:
I want to use below formula:
Problem Picture http://upcity.ir/images2/70779463920887716017.jpg
for a set of $3$ equations, first phrase is a $12\times1$ matrix, and $r$ matrix is $12\times1$. So phrases $P$ and $q$ (in above picture) should be $1\times1$ . What would I put instead of $f(x_{n+1},y_{n+1})$ ? In other words, how I use above equation?
Thank you for your help.