I am trying to solve a system of ordinary differential equations as follows:
z1' = 2*z1 + 2*z4 z2' = z2 + 2*z5 z3' = z3 + z6 z4' = z4 - z1 z5' = z5 + 3*z2 z6' = z6 - 2*z3
with boundary conditions of
z2(0) = z4(0) = z6(0) = 0 z2(2) = 1, z4(2) = 1, z6(2) = 3
Does anyone know of an effective algorithm that could solve this problem? Currently I am trying to do a shooting method and guessing the initial values for z1, z3, and z5. Is it possible to update all of the inital guesses for shooting at the same time? If so, how would I do it? If there is a better way to approach it please let me know.