Parallel numerical solution of PDEs using Taylor series method

The contribution deals with the parallel numerical solution of partial differential equations. The partial differential equation is solved using the method of lines by discretizing the spatial domain using finite differences. The resulting system of ordinary differential equations is solved in parallel by a higher-order Taylor series-based numerical method. The numerical solution obtained using the method is compared with the state-of-the-art PETSc solvers. The simulation experiments were performed on the Barbora supercomputer cluster, IT4Innovations National Supercomputing Center, Ostrava, Czech Republic. The results are evaluated based on performance and parallel cost metrics. The results show that Taylor-series-based method can significantly overperform the state-of-the-art solvers.