The Exact Formulation of the Inverse of the Tridiagonal Matrix for Solving the 1D Poisson Equation with the Finite Difference Method

Serigne Bira Gueye

doi:10.4236/jemaa.2014.610030

Home > Journals > Engineering | Physics & Mathematics > JEMAA

JEMAA> Vol.6 No.10, September 2014

Share This Article:

Open Access

The Exact Formulation of the Inverse of the Tridiagonal Matrix for Solving the 1D Poisson Equation with the Finite Difference Method

Abstract Full-Text HTML XML

Download as PDF (Size:384KB) PP. 303-308

DOI: 10.4236/jemaa.2014.610030 3,572 Downloads 4,317 Views Citations

Author(s) Leave a comment

Serigne Bira Gueye^*

Affiliation(s)

Département de Physique, Faculté des Sciences et Techniques, Université Cheikh Anta Diop, Dakar-Fann, Sénégal.

ABSTRACT

A new method for solving the 1D Poisson equation is presented using the finite difference method. This method is based on the exact formulation of the inverse of the tridiagonal matrix associated with the Laplacian. This is the first time that the inverse of this remarkable matrix is determined directly and exactly. Thus, solving 1D Poisson equation becomes very accurate and extremely fast. This method is a very important tool for physics and engineering where the Poisson equation appears very often in the description of certain phenomena.

KEYWORDS

1D Poisson Equation, Finite Difference Method, Tridiagonal Matrix Inversion, Thomas Algorithm, Gaussian Elimination, Potential Problem

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Gueye, S. (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 Applications, 6, 303-308. doi: 10.4236/jemaa.2014.610030.

References

[1]	Conte, S.D. and de Boor, C. (1981) Elementary Numerical Analysis: An Algorithmic Approach. 3rd Edition, McGrawHill, New York, 153-157.

[2]	Leveque, R.J.E. (2007) Finite Difference Method for Ordinary and Partial Differential Equations, Steady State and Time Dependent Problems. SIAM, 15-16. http://dx.doi.org/10.1137/1.9780898717839

[3]	Mathews, J.H. and Kurtis, K.F. (2004) Numerical Methods Using Matlab. 4th Edition, Prentice Hall, Upper Saddle River, 323-325, 339-342.