Numerical Methods for Engineering Computation in Python

Collection of Python scripts used in AME-3723: Numerical Methods for Engineering Computation for obtaining and/or validating homework answers.

Supported methods for approximating the root(s) of an equation:

Bracketing Methods: (Slower but always converge assuming f(x) = 0 is bounded by a and b)

• Bisection method (Requires an initial range to search for a root within, f(x) = 0 must be bounded by a and b)
• False Position (Linear interpolation) method (Requires an initial range to search for a root within, f(x) = 0 must be bounded by a and b)

Open Methods: (Faster but do not always converge)

• Newton-Raphson method: (Requires the derivative to be known or approximated and an inital guess must be made)
• Secant method: (Does not require a derivative but does require two inital guesses)

Usage

Replace the 'f' parameter at the end of each script with the function you are attempting to find the root of. Replace all other parameters as necessary.

Ti-nspire library usage:

• Load the '*.tns' file onto your calculator via the Ti-nspire student software.
• Click 'menu', '1: Actions', '7: Library', "1: Refresh Libraries", and wait for this to complete
• Click the book icon (below the delete key) then click 6 to open the user-defined library tab
• Scroll down to 'numericalmethods'

Ti-nspire library examples:

Bisection Method:

• bisectionmethod(4.998*10^(−8)x^(2)-1.15710^(−13)x^(4)-2.99910^(−3),200,300,5)
• First parameter is F(x) that you want to find the root(s) of
• Second parameter is a, the lower bounds containing the solution
• Third parameter is b, the upper bounds containing the solution
• Fourth parameter is the number of iterations to complete

False Position Method:

• falseposmethod(cos(x)-0.8*x^(2),0.5,1.5,5)
• First parameter is F(x) that you want to find the root(s) of
• Second parameter is a, the lower bounds containing the solution
• Third parameter is b, the upper bounds containing the solution
• Fourth parameter is the number of iterations to complete

Newton's Method:

• newtonsmethod(e^(−0.5x)(4-x)-2,2,5)
• First parameter is F(x) that you want to find the root(s) of -- Derivatives will be calculated automatically (requires CAS)
• Second parameter is the inital guess
• Third parameter is the number of iterations to complete

Secant Method:

• secantmethod(x-(2*e^(−x)),0,1,5)
• First parameter is F(x) that you want to find the root(s) of
• Second parameter is x_1, the first guess
• Third parameter is x_2, the second guess
• Fourth parameter is the number of iterations to complete