IndexError index 1 is out of bounds for axis 0 with size 1 ForwardEuler

Question

I am numerically solving for x t  for a system of first order differential equations  The system is   dy dt  C     -K  x  M A   I have implemented the Forward Euler method to solve this problem as follows  Here is my code   import matplotlib import numpy as np from numpy import   from numpy import linspace from matplotlib import pyplot as plt   C 3 K 5 M 2 A 5  ------------------------------------------------------------------------------ def euler  f x0 t       n len  t      x np array   x0 n       for i in xrange  n-1           x i 1    x i      t i 1  - t i      f  x i   t i        return x     ---------------------------------------------------------------------------------           if   name       main         from pylab import        def f x t            return  C    -K x  M A       a b  0 0 10 0      n 200     x0 -1 0     t linspace  a b n        numerical solutions     x euler euler f x0 t        compute true solution values in equal spaced and unequally spaced cases     x -C K      figure     plt plot  t x euler   b       xlabel        ylabel        legend   Euler        show     M 2 A 5  ---------------------------------------------------------------------------- def euler  f x0 t       n len  t      x np array   x0 n       for i in xrange  n-1           x i 1    x i      t i 1  - t i      f  x i   t i        return x     ---------------------------------------------------------------------------           if   name       main         from pylab import        def f x t            return  C    -K x  M A       a b  0 0 10 0      n 200     x0 -1 0     t linspace  a b n        numerical solutions     x euler euler f x0 t        compute true solution values in equal spaced and unequally spaced cases     x -C K      figure     plt plot  t x euler   b       xlabel        ylabel        legend   Euler        show     I get following Traceback   Traceback  most recent call last     File  C  Python27 testeuler py   line 50  in  lt module gt      x euler euler f x0 t    File  C  Python27 testeuler py   line 28  in euler     x i 1    x i      t i 1  - t i      f  x i   t i    IndexError  index 1 is out of bounds for axis 0 with size 1   I don  t understand what is probably wrong I already looked up after solved questions  but it doesn  t help me along Can you find my error  I am using following code as an orientation      def euler  f  x0  t         n   len  t       x   numpy array   x0    n       for i in xrange  n - 1            x i 1    x i      t i 1  - t i      f  x i   t i         return x if   name         main         from pylab import        def f  x  t            return x   numpy sin  t        a  b     0 0  10 0       x0   -1 0      n   51     t   numpy linspace  a  b  n        x euler   euler  f  x0  t     My goal is to plot the function

User · Accepted Answer

The problem  as the Traceback says  comes from the line  x i 1    x i      t i 1  - t i      f  x i   t i     Let s replace it in its context    x is an array equal to  x0   n   so its length is 1 you re iterating from 0 to n-2  n doesn t matter here   and i is the index  In the beginning  everything is ok  here there s no beginning apparently          but as soon as i   1  gt   len x   lt    i  gt   0  the element x i 1  doesn t exist  Here  this element doesn t exist since the beginning of the for loop    To solve this  you must replace x i 1    x i      t i 1  - t i      f  x i   t i    by x append x i      t i 1  - t i      f  x i   t i

User · Answer

The problem is with your line  x np array   x0 n     Here you define x as a single-item array of -200 0  You could do this   x np array   x0   n    or this   x np zeros  n      x0   Note  your imports are quite confused  You import numpy modules three times in the header  and then later import pylab  that already contains all numpy modules   If you want to go easy  with one single  from pylab import     line in the top you could use all the modules you need

[python] IndexError: index 1 is out of bounds for axis 0 with size 1/ForwardEuler

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