Do you know how to implement the evolution scheme of the DE using a matrix approach?
Using the 4th-order Runge-Kutta method, I have been able to successfully compute the solutions to a coupled pair of two first order differential equations using the following formula:
When solving systems of ODEs with more than two equations I am unsure if I am properly expanding on the above ideas.
For example I am trying to find a system of three first order equations:
da/dx = 2bc + 3a
db/dx = 4ac +11b
dc/dx = 5ab + c
Using and expanding on the equations above would I be correct in the following:
K0 = 2bc + 3a
L0 = 4ac +11b
M0 = 5ab + c
k1 = 2*(b+(L0)/2)*(c+(M0)/2) + 3*(a+(K0)/2)
L1 = 4*(a+(K0)/2)*(c+(M0)/2) + 11*(b+(L0)/2)
M1 = 5*(a+(K0)/2)*(b+(L0)/2) + (c+(M0)/2)
And so on for K2,L2,M2 etc?
Hopefully that's fairly readable.
Is this the correct approach to take or am I making a glaring error somewhere?