INTEGRAL TRANSFORM ANALYSIS OF MULTIDIM ENSIONAL EIGENVALUE PROBLEMS WITHIN IRREGULAR DOMAINS

Abstract

The generalized integral transform technique (GITT) is employed in obtaining formal solutions for eigenvalue problems of the Sturm-Liouville type, described by multidimensional partial differential models within irregularly shaped domains. The successive elimination of independent variables in the appropriate order through integral transformations produces the associated algebraic eigenvalue problem, which is then readily solved by algorithms from scientific subroutine libraries. A representative example of the known exact solution is presented, of particular interest to the field of heat and mass diffusion, for validation purposes.