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Problem Parameters: The function that you build needs to take in

  • The current value of the independent variable (x)
  • The current values of the dependent variables (y) <-- (list)
  • The step-size of the independent variable (h)
  • The function which calculates the derivatives depending on x and y. <-- will return a list

The function will return the values of the dependent variables (y) at x+h

We are given a tester code and when mine runs I'm getting the "list index out of range" error

My code is: 

def rk4( x, y, h, derivs ):
# ... Note, y is a list, ynew is a list, derivs returns a list of derivatives
n = len( y )
k1 = derivs( x, y )
ym = [ ]
ye = [ ]
slope = [ ]
ynew = [ ]

for i in range( n ):
    ym[ i ] = y[ i ] + k1[ i ] * h / 2 
    return ym

k2 = derivs( (x + h / 2), ym )

for i in range( n ):
    ym[ i ] = y[ i ] + k2[ i ] * h / 2
    return ym

k3 = derivs( (x + h / 2), ym )

for i in range( n ):
    ye.append( y[ i ] + k3[ i ] * h )
    return ye

k4 = derivs( (x + h), ye )

for i in range( n ):
    slope.append( (k1[ i ] + 2 * (k2[ i ] + k3[ i ]) + k4[ i ]) / 6 )
    ynew.append( y[ i ] + slope[ i ] * h )
    return ynew

x = x + h

return ynew

Tester Code:

if __name__ == '__main__':

# This is a spring/mass/damper system.
# The system oscillates and the oscillations should become smaller over time for positive stiffness and damping values
stiffness = 4;  #
damping = 0.5;


def derivs(t, y):
    return [y[1], -stiffness * y[0] - damping * y[1]]


y = [1, 4]
n = 50
tlow = 0
thigh = 10
h = (thigh - tlow) / (n - 1)
for ii in range ( n ):
    t = tlow + ii * h
    y = rk4 ( t, y, h, derivs )
Lutz Lehmann
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Shiaa
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1 Answers1

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Python, contrary to Matlab, will not automatically increase a list when its bounds are violated. Use

ym = n*[0.0]

etc. to initialize a list of the correct length.

Or just use list operations, then no initialization is necessary

ym = [ y[i]+0.5*h*k1[i] for i in range(n) ]

or

ym = [ yy+0.5*h*kk for yy,kk in zip(y,k1) ]

etc.

Also, remove the return statements where you do not want to leave the function.

Lutz Lehmann
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