Euler's Method, Runge-Kutta, and Simpson's Rule
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4 Terms
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Standard Euler’s Method
xn+1 = xn = h
yn+1 = yn + h( f(xn, yn)
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Improved Euler’s Method
xn+1 = xn = h
un+1 = yn + h( f(xn, un)
k1 = f(xn, yn)
k2 = yn(xn+1, un+1)
yn+1 = yn + h ((k1 + k2)/2)
3
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Simpson’s Rule
integral a - b = (b-a)/6(y’(xn) + 4y’(xn + 1/2h) + y’(xn + h)
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Runge-Kutta Method
yn+1 = yn+h/6 (k1 + 2k2 + 2k3 + k4)
k1 = f(xn, yn)
k2 = f(xn + 1/2h, yn + 1/2h k1)
k3 = f(xn + 1/2h, yn + 1/2h k2)
k4 = f(xn + h, yn +h k3)