I am trying to solve six first order coupled ODE's, two of these are associated with a heat balance of a catalyst pellet, and four are mass balances.
I have been trying to solve these equations using Orthogonal collocation (rather than using those algorithms used by NDSolve in Mathematica - my hope is to speed up the computation). I have found a lot of examples and lectures on using Orthogonal collocation to solve a single ordinary differential equation, however, I have not come across anything in the literature, as how to solve these equations when they are coupled.
I therefore wanted to ask if anyone has experience with this, and could possibly point me toward some literature, and/or worked examples, or explain the twist on how to migrate from a single ODE to coupled ODE's.
Best Regards