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

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  • Mohammad Masjed-Jamei
  • Mehdi Dehghan

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.

Suggested Citation

  • Mohammad Masjed-Jamei & Mehdi Dehghan, 2006. "Application of zero eigenvalue for solving the potential, heat, and wave equations using a sequence of special functions," Mathematical Problems in Engineering, Hindawi, vol. 2006, pages 1-9, February.
    • Handle: RePEc:hin:jnlmpe:064132
    DOI: 10.1155/MPE/2006/64132
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