Application of zero eigenvalue for solving the potential, heat, and wave equations using a sequence of special functions
type: Item
instance of: scholarly article
title: Application of zero eigenvalue for solving the potential, heat, and wave equations using a sequence of special functions
zbMATH Open document ID: 1200.35058
DOI: 10.1155/MPE/2006/64132
author: Mohammad Masjed-Jamei
author: Mehdi Dehghan
published in: Mathematical Problems in Engineering
publication date: 2010-12-01T00:00:00Z
review text: Summary: In the solution of boundary value problems, usually zero eigenvalue is ignored. This case also happens in calculating the eigenvalues of matrices, so that we would often like to find the nonzero solutions of the linear system \(AX=\lambda X\) when \(\lambda\neq0\). But \(\lambda=0\) implies that \(\text{det} A=0\) for \(X\neq0\) and then the rank of matrix \(A\) is reduced at least one degree. This comment can similarly be stated for boundary value problems. In other words, if at least one of the eigens of equations related to the main problem is considered zero, then one of the solutions will be specified in advance. By using this note, first we study a class of special functions and then apply it for the potential, heat, and wave equations in spherical coordinate. In this way, some practical examples are also given.
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 65N99
zbMATH DE Number: 5822515
MaRDI profile type: Publication
cites work: Q5508799
cites work: Orthogonal rational functions on a semi-infinite interval
cites work: Q4039835
description: scientific article; zbMATH DE number 5822515