How to make Runge Kutta method for system of non linear equations in this Matrix form. Matrices A3, B3 and B4 are functions of matrix X3. Initial conditions are X1=X2=X3=X4=0 and system is here
$ \frac{d}{dt}\left( \begin{array}{c} \text{X1} \\ \text{X2} \\ \text{X3} \\ \text{X4} \end{array} \right)=\left( \begin{array}{cccc} -\text{A2} & -\text{A1} & -\text{A3} & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ -\text{B3} & 0 & -\text{B2}-\text{B4} & \text{B1} \end{array} \right).\left( \begin{array}{c} \text{X1} \\ \text{X2} \\ \text{X3} \\ \text{X4} \end{array} \right)+\left( \begin{array}{c} 0 \\ 0 \\ 0 \\ \text{B5} \end{array} \right).\left( \begin{array}{cccc} 0 & 0 & 0 & 1 \end{array} \right) $
$ \text{X1}=\left( \begin{array}{c} \text{x11} \\ \text{x12} \\ \text{x13} \end{array} \right); $
$ \text{X2}=\left( \begin{array}{c} \text{x21} \\ \text{x22} \\ \text{x23} \end{array} \right); $
$ \text{X3}=\left( \begin{array}{c} \text{x31} \\ \text{x32} \\ \text{x33} \end{array} \right); $
$ \text{X4}=\left( \begin{array}{c} \text{x41} \\ \text{x42} \\ \text{x43} \end{array} \right); $
Where we have matrices
$\text{A1}=\left( \begin{array}{ccc} \frac{640576501799}{76356} & 0 & \frac{311934265235}{57839} \\ 0 & \frac{1285802795705}{40871} & 0 \\ \frac{388065734765}{30838} & 0 & \frac{523620702496}{6935} \end{array} \right);$
$ \text{A2}=\left( \begin{array}{ccc} \frac{980000000000000}{1168149} & 0 & \frac{210000000000000}{389383} \\ 0 & \frac{1225000000000000}{389383} & 0 \\ \frac{490000000000000}{389383} & 0 & \frac{2940000000000000}{389383} \end{array} \right);$
$ \text{A3}=\left( \begin{array}{ccc} 0 & \frac{152600000000000000 \text{x31}}{14532941709}+\frac{76300000000000000 \text{x33}}{4844313903} & 0 \\ 0 & \frac{953750000000000000 \text{x32}}{14532941709} & 0 \\ 0 & \frac{76300000000000000 \text{x31}}{4844313903}+\frac{1068200000000000000 \text{x33}}{4844313903} & 0 \end{array} \right);$
$ \text{B1}=\left( \begin{array}{ccc} \frac{5874951206}{12955399} & 0 & \frac{3212738087}{4414317} \\ 0 & \frac{8215070163}{2795011} & 0 \\ \frac{8400845503}{6412667} & 0 & \frac{6246501886}{520165} \end{array} \right); $
$ \text{B2}=\left( \begin{array}{ccc} \frac{14850000000000}{327471103} & 0 & \frac{71500000000000}{982413309} \\ 0 & \frac{96250000000000}{327471103} & 0 \\ \frac{42900000000000}{327471103} & 0 & \frac{393250000000000}{327471103} \end{array} \right); $
$ \text{B3}=\left( \begin{array}{ccc} 0 & -\frac{180000000000000000 \text{x31}}{1027581737}-\frac{40000000000000000 \text{x33}}{79044749} & 0 \\ 0 & -\frac{700000000000000000 \text{x32}}{440392173} & 0 \\ 0 & -\frac{40000000000000000 \text{x31}}{79044749}-\frac{660000000000000000 \text{x33}}{79044749} & 0 \end{array} \right); $
$ \text{B4}=\left( \begin{array}{ccc} \frac{55687500000000000000 \left(\frac{16 \text{x31}^2}{11781}-\frac{640 \text{x31} \text{x33}}{2909907}\right)}{327471103}+\frac{160875000000000000000 \left(\frac{16 \text{x31} \text{x33}}{11781}-\frac{640 \text{x33}^2}{2909907}\right)}{327471103} & \frac{540900000000000000000 \text{x31} \text{x32}}{9625358130479}+\frac{120200000000000000000 \text{x32} \text{x33}}{740412163883} & \frac{55687500000000000000 \left(-\frac{640 \text{x31}^2}{2909907}+\frac{2456 \text{x31} \text{x33}}{14549535}\right)}{327471103}+\frac{160875000000000000000 \left(-\frac{640 \text{x31} \text{x33}}{2909907}+\frac{2456 \text{x33}^2}{14549535}\right)}{327471103} \\ \frac{505312500000000000000 \left(\frac{16 \text{x31} \text{x32}}{11781}-\frac{640 \text{x32} \text{x33}}{2909907}\right)}{327471103} & \frac{2103500000000000000000 \text{x32}^2}{4125153484491} & \frac{505312500000000000000 \left(-\frac{640 \text{x31} \text{x32}}{2909907}+\frac{2456 \text{x32} \text{x33}}{14549535}\right)}{327471103} \\ \frac{160875000000000000000 \left(\frac{16 \text{x31}^2}{11781}-\frac{640 \text{x31} \text{x33}}{2909907}\right)}{327471103}+\frac{2654437500000000000000 \left(\frac{16 \text{x31} \text{x33}}{11781}-\frac{640 \text{x33}^2}{2909907}\right)}{327471103} & \frac{120200000000000000000 \text{x31} \text{x32}}{740412163883}+\frac{1983300000000000000000 \text{x32} \text{x33}}{740412163883} & \frac{160875000000000000000 \left(-\frac{640 \text{x31}^2}{2909907}+\frac{2456 \text{x31} \text{x33}}{14549535}\right)}{327471103}+\frac{2654437500000000000000 \left(-\frac{640 \text{x31} \text{x33}}{2909907}+\frac{2456 \text{x33}^2}{14549535}\right)}{327471103} \end{array} \right); $
$ \text{B5}=\left( \begin{array}{c} \frac{37125000}{3241} \\ 0 \\ \frac{107250000}{3241} \end{array} \right); $