  This paper presents an experimental performance study of implementations of
three different types of algorithms for solving band matrix systems of linear
algebraic equations (SLAEs) after parabolic nonlinear partial differential
equations -- direct, symbolic, and iterative, the former two of which were
introduced in Veneva and Ayriyan (arXiv:1710.00428v2). An iterative algorithm
is presented -- the strongly implicit procedure (SIP), also known as the Stone
method. This method uses the incomplete LU (ILU(0)) decomposition. An
application of the Hotelling-Bodewig iterative algorithm is suggested as a
replacement of the standard forward-backward substitutions. The upsides and the
downsides of the SIP method are discussed. The complexity of all the
investigated methods is presented. Performance analysis of the implementations
is done using the high-performance computing (HPC) clusters "HybriLIT" and
"Avitohol". To that purpose, the experimental setup and the results from the
conducted computations on the individual computer systems are presented and
discussed.
