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Semi-Analytical Solution of the 1D Helmholtz Equation, Obtained from Inversion of Symmetric Tridiagonal Matrix

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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.
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Gueye, S. (2014) Semi-Analytical Solution of the 1D Helmholtz Equation, Obtained from Inversion of Symmetric Tridiagonal Matrix. Journal of Electromagnetic Analysis and Applications, 6, 425-438. doi: 10.4236/jemaa.2014.614044. 
 

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http://dx.doi.org/10.1088/0305-4470/29/7/020
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[3] Epp, S.S. (2011) Discrete Mathematics with Applications. 4th Edition, Brooks/Cole Cengage Learning, Bostion, 317-327.
[4] Gueye, S.B. (2014) The Exact Formulation of the Inverse of the Tridiagonal Matrix for Solving the 1D Poisson Equation with the Finite Difference Method. Journal of Electromagnetic Analysis and Application, 6, 303-308.
http://dx.doi.org/10.4236/jemaa.2014.610030
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http://dx.doi.org/10.1137/1.9780898717839                    eww141223lx
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