TY - JOUR
A2 - Cen, Song
AU - Luck, Rogelio
AU - Zdaniuk, Gregory J.
AU - Cho, Heejin
PY - 2015
DA - 2015/10/15
TI - An Efficient Method to Find Solutions for Transcendental Equations with Several Roots
SP - 523043
VL - 2015
AB - This paper presents a method for obtaining a solution for all the roots of a transcendental equation within a bounded region by finding a polynomial equation with the same roots as the transcendental equation. The proposed method is developed using Cauchy’s integral theorem for complex variables and transforms the problem of finding the roots of a transcendental equation into an equivalent problem of finding roots of a polynomial equation with exactly the same roots. The interesting result is that the coefficients of the polynomial form a vector which lies in the null space of a Hankel matrix made up of the Fourier series coefficients of the inverse of the original transcendental equation. Then the explicit solution can be readily obtained using the complex fast Fourier transform. To conclude, the authors present an example by solving for the first three eigenvalues of the 1D transient heat conduction problem.
SN - 2356-7007
UR - https://doi.org/10.1155/2015/523043
DO - 10.1155/2015/523043
JF - International Journal of Engineering Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -