#!/usr/bin/env python
# coding: utf-8

# # Homework Set 11

# In[2]:


get_ipython().run_line_magic('pylab', 'inline')


# ## Problem 1:
# 
# * Applying the forward Euler's scheme to the second order ODE:
# 
# $$
# y'' + (\lambda+1)y' + \lambda y = 0, \;\; y(0) = 1, \;\; y'(0) = \lambda - 2, \;\; \lambda >> 1.
# $$
# 
# Rewrite it as a system of first order ODEs. Find the region of absolute stability. (Hint: find the eigenvalue decomposition of the coefficient matrix, and the region of absolute stability is the domain where the step size is chosen so that each eigen value satisfies the condition for the 1D ODE.)
#      
#