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Math Help - Solving a system of ODEs using Runge-Kutta

  1. #1
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    Solving a system of ODEs using Runge-Kutta

    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?
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  2. #2
    MHF Contributor
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    Re: Solving a system of ODEs using Runge-Kutta

    Hey BMor.

    Do you know how to implement the evolution scheme of the DE using a matrix approach?
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