TITLE:
Semi-Analytical Solution of the 1D Helmholtz Equation, Obtained from Inversion of Symmetric Tridiagonal Matrix
AUTHORS:
Serigne Bira Gueye
KEYWORDS:
Helmholtz Equation, Tridiagonal Matrix, Linear Homogeneous Recurrence Relation
JOURNAL NAME:
Journal of Electromagnetic Analysis and Applications,
Vol.6 No.14,
December
22,
2014
ABSTRACT: An interesting semi-analytic solution is given for the Helmholtz
equation. This solution is obtained from a rigorous discussion of the
regularity and the inversion of the tridiagonal symmetric matrix. Then,
applications are given, showing very good accuracy. This work provides also the
analytical inverse of the skew-symmetric tridiagonal matrix.