FORTRAN source code of a package of subroutines to evaluate eigenvalues of Sturm Liouville problems arising when solving heat conduction problems in Cartesian and cylindrical coordunates. The geometry covered include slab, solid and hollow cylinders for problems subjected to every combination of boundary conditions of the first, second and third kind (Dirichlet, Neumann and Robin). 


The underlying theory and the printout of the first version of the routines can be found in



A.J. Nowak, R.A. Białecki and K. Kurpisz: Evaluating eigenvalues for boundary value problems of heat conduction in rectangular and cylindrical coordinate systems, International Journal for Numerical Methods in Engineering, 24: 2, (1987), pp. 419–445


Compared to the published version, some bugs are fixed and the programming language upgraded from FORTRAN IV to FORTRAN 95.  


The material is accompanying a chapter entitled Green's Function in Transient Heat Conduction published in Encyclopedia of Thermal Stress, R.H. Hetnarski (edt), Springer 2013.


Below there is a set of FORTRAN 95 files, which compose the program for calculating eigenvalues of the boundary heat conduction problems in a slab, cylinder and hollow cylinder, subjected to all kinds of boundary conditions.

  • main program file (download)
  • procedures used for the slab geometry (download)
  • procedures used for the cylinder and hollow cylinder geometry (download)
  • routines describing the transcendental equations (download)
  • procedure solving a nonlinear algebraic equation (download)
  • routines for calculationg Bessel functions (download

All files of the program compressed as a zip archive (download)