○ 4^th-order Runge-Kutta(runge-kutta-4.rb)

# ルンゲクッタで積分
require "derivative"

def integral(time, dt, pv, pv0)

　if @rfirst == nil
　　@rfirst = false
　　@w = pv.dup
　end

　d1 = derivative(pv, pv0)
　@w.spect = pv.spect + d1 * dt / 2.0
　d2 = derivative(@w, pv0)
　@w.spect = pv.spect + d2 * dt / 2.0
　d3 = derivative(@w, pv0)
　@w.spect = pv.spect + d3 * dt
　d4 = derivative(@w, pv0)

　pv.spect = pv.spect + (d1 + d2 * 2.0 + d3 * 2.0 + d4) / 6.0 * dt
　time = time + dt

　return time, pv

end

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