A technique for developing complete orthonormal basis sets using general solutions of Bessel's differential equation

摘要

A technique is discussed for the development of a complete orthonormal basis set for boundary value problems satisfying the Dirichlet boundary condition, where the basis functions are general solutions of Bessel's differential equation. A classical formulation for the existence and completeness of the basis sets, along with algorithms for computing the eigenvalues and eigenfunctions that describe the basis sets, is presented. The technique is applied to a sample boundary value problem and graphs of the basis functions are presented.