PSC Math 216-01

Computer Programs for Differential Equations

1. Sage is a free, open-source, computer algebra system that can be run online without installing any software on your personal computer.  It can also be downloaded and installed, but I don't recommend this option for students.  Once you've created a Sage account, you can upload and use the following notebooks:

• Direction_Fields.sws - plot slope fields for a 1st-order DE
• Euler.sws - use Euler's method or improved Euler's method to approximate solutions
• DE_Exact_Solution.sws - Symbolically find exact solutions of 1st order DEs
• RK4.sws - use the classic 4th-order Runge-Kutta method to approximate solutions
• Classic_RK4sys.sws - use the classic 4th-order Runge-Kutta method to approximate solutions of systems of ODEs

2. Lua is a free, open-source programming language that is available for almost every conceivable platform.  It is perfect for the type of programming we will need.

• euler.lua - use Euler's method to approximate solutions
• ieuler.lua - use the improved Euler method to approximate solutions
• rk4.lua - use the classic 4th-order Runge-Kutta method to approximate solutions
• rk4sys.lua - use the classic 4th-order Runge-Kutta method to approximate solutions of systems of ODEs
• rk5.lua - use Butcher's 5th-order Runge-Kutta method to approximate solutions

3. Python is a free, open-source programming language that is steadily gaining popularity for use with scientific applications.  Like Lua, it is perfect for the programming we will need.  If you take the time to learn a bit of the Python language, it should be very easy to convert the Lua programs above to Python.  Sage has a built-in Python interpreter---if you use Sage, there is no need to install Python.

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