An facile Fortran-95 algorithm to simulate complex instabilities in three-dimensional hyperbolic systems

It is well know that the simulation of fractional systems is a difficult task from all points of view. In particular, the computer implementation of numerical algorithms to simulate fractional systems of partial differential equations in three dimensions is a hard task which has no been solved satisfactorily. Here, we provide a Fortran-95 code to solve systems of hyperbolic (fractional o non-fractional) partial differential equations that generalize various known models from physics, chemistry and biology. The algorithm is easy to implement in any other computer language by any scientist with minimal knowledge on scientific programming. The computer implementation exploits the advantages of the efficient matrix algebra already available in Fortran and other languages. This code is susceptible to be compiled in parallel using OpenMP, whence it follows that the computer time can be substantially reduced. The details of the mathematical model solved by this code can be found in Macías-Díaz, J. E. Computer Physics Communications (2020):107383, https://doi.org/10.1016/j.cpc.2020.107383