How to solve non linear system of differential equations in Mathematica using Finite difference or other method [closed]

Question

Can you help me about system of equations. I wrote in subject Finite difference or other method, because I know that it is working good for this type of equations. I need a code in Mathematica for solving this non linear system. I will want to write just somebody who already have a experience in solving the non linear differential equations and help with code in Mathematica. Not to put just NDSolve and this is it. Also, the answer will be acceptable if the code is working. System is

   \[DifferentialD]X1/\[DifferentialD]t = -A1.X2 - A2.X1 - A3.X3;
   \[DifferentialD]X2/\[DifferentialD]t = X1;
   \[DifferentialD]X3/\[DifferentialD]t = X4;
   \[DifferentialD]X4/\[DifferentialD]t = B1.X4 - B2.X3 - B3.X1 - B4.X3 + B5; 

Initial conditions (t=0) we have X1=X2=X3=X4=0 where

   X1 = {{x11}, {x12}, {x13}};
   X2 = {{x21}, {x22}, {x23}};
   X3 = {{x31}, {x32}, {x33}};
   X4 = {{x41}, {x42}, {x43}};

   A1 = {{640576501799/76356, 0, 311934265235/57839}, {0, 1285802795705/
40871, 0}, {388065734765/30838, 0, 523620702496/6935}};
   A2 = {{980000000000000/1168149, 0, 210000000000000/389383}, {0, 
1225000000000000/389383, 0}, {490000000000000/389383, 0, 
2940000000000000/389383}};
   A3 = {{0, (152600000000000000 x31)/14532941709 + (
 76300000000000000 x33)/4844313903, 0}, {0, (
953750000000000000 x32)/14532941709, 
0}, {0, (76300000000000000 x31)/4844313903 + (
 1068200000000000000 x33)/4844313903, 0}};
   B1 = {{5874951206/12955399, 0, 3212738087/4414317}, {0, 8215070163/
2795011, 0}, {8400845503/6412667, 0, 6246501886/520165}};
   B2 = {{14850000000000/327471103, 0, 71500000000000/982413309}, {0, 

96250000000000/327471103, 0}, {42900000000000/327471103, 0, 393250000000000/327471103}};

 B3 = {{0, -((180000000000000000 x31)/1027581737) - (
 40000000000000000 x33)/79044749, 
0}, {0, -((700000000000000000 x32)/440392173), 
0}, {0, -((40000000000000000 x31)/79044749) - (
 660000000000000000 x33)/79044749, 0}};


    B4 = {{(55687500000000000000 ((16 x31^2)/11781 - (640 x31 x33)/
      2909907))/327471103 + (
   160875000000000000000 ((16 x31 x33)/11781 - (640 x33^2)/
    2909907))/327471103, (540900000000000000000 x31 x32)/
 9625358130479 + (120200000000000000000 x32 x33)/740412163883, (
 55687500000000000000 (-((640 x31^2)/2909907) + (2456 x31 x33)/
    14549535))/327471103 + (
 160875000000000000000 (-((640 x31 x33)/2909907) + (2456 x33^2)/
    14549535))/327471103}, {(
505312500000000000000 ((16 x31 x32)/11781 - (640 x32 x33)/
   2909907))/327471103, (2103500000000000000000 x32^2)/
4125153484491, (
505312500000000000000 (-((640 x31 x32)/2909907) + (2456 x32 x33)/
   14549535))/
327471103}, {(
 160875000000000000000 ((16 x31^2)/11781 - (640 x31 x33)/
    2909907))/327471103 + (
 2654437500000000000000 ((16 x31 x33)/11781 - (640 x33^2)/
    2909907))/327471103, (120200000000000000000 x31 x32)/
 740412163883 + (1983300000000000000000 x32 x33)/740412163883, (
 160875000000000000000 (-((640 x31^2)/2909907) + (2456 x31 x33)/
    14549535))/327471103 + (
 2654437500000000000000 (-((640 x31 x33)/2909907) + (2456 x33^2)/
    14549535))/327471103}};
  B5 = {{37125000/3241}, {0}, {107250000/3241}};