Application of zero eigenvalue for solving the potential, heat, and wave equations using a sequence of special functions

Mohammad Masjed-Jamei and Mehdi Dehghan

Mathematical Problems in Engineering, 2006, vol. 2006, 1-9

Abstract:

In the solution of boundary value problems, usually zeroeigenvalue is ignored. This case also happens in calculating theeigenvalues of matrices, so that we would often like to find thenonzero solutions of the linear system A X = λ X when λ ≠ 0 . But λ = 0 implies that det A = 0 for X ≠ 0 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 relatedto the main problem is considered zero, then one of the solutionswill be specified in advance. By using this note, first we study aclass 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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:064132

DOI: 10.1155/MPE/2006/64132

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