Finding The Zeros of Transcendental Equations Using a Fixed Point Iteration Method

by Arjun Gajjar

Submitted : Fall 2015

Future civil engineering courses, like thermodynamics and fluid mechanics, will ask students to solve heat transfer equations. Therefore it is important to have a basic understanding of how different forms of mathematics can be used to solve certain parts of thermodynamics problems. For example, when solving a quenching problem where a cylinder is quenched in a liquid, first the zeros of the Bessel function are needed to define the Eigenvalues and Eigenfunctions for the problem. The Eigenvalues and Eigenfunctions are then used along with a Fourier series representation to write the equation that shows heat transfer throughout cylindrical coordinates.

In order to find the zeros we will be using the Fixed point iteration method. The fixed point iteration method is tool that can be used to solve transcendental equations by inputting the output of an equation back into its original formula. Some functions may take more successive terms before accurately converging, but in general fixed point iteration is a relatively easy method of finding the roots of an equation.

[ Back ]