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Runge-Kutta 4 for systems of equations. ordinary-differential-equations numerical-methods. 3,982. You need to build a system of four first order coupled differential

Now I know that for two general 1st order ODE's dy dx = f(x, y, z)dz dx = g(x, y, z) The 4th order Runge-Kutta formula's for a system of 2 ODE's are:

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Derivation of the Runge–Kutta fourth-order method In general a Runge–Kutta method of order s {\displaystyle s} can be written as: y t + h = y t + h ⋅ ∑ i = 1 s a i k i + O ( h s + 1 ) , {\displaystyle

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You need to build a system of four first order coupled differential equations. Given that $u = x'$ and $v = y'$. So then the first set of equations becomes $$u' = f(x, y, u, v)$$ $$v' = g(x, y, u, v)$$

L4 = h * f ( t (i)+h , x (i)+K3 , y (i)+L3, z (i)+M3); M4 = h * g ( t (i)+h , x (i)+K3 , y (i)+L3, z (i)+M3); x (i+1) = x (i)+1/6* (K1+2*K2+2*K3+K4); y (i+1) = y (i)+1/6* (L1+2*L2+2*L3+L4); z (i+1) = z (i)+1/6* (M1+2*M2+2*M3+M4); end

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