Parallel solution of partial differential equations using Taylor series method

The contribution focuses on the parallel numerical solution of partial differential equations. The original problem is transformed into the system of ordinary differential equations using the method of lines. The resulting system of ordinary differential equations is solved by a higher-order numerical method based on the Taylor series. The numerical solution is compared with the state-of-the-art PETSc solvers. The results show that Taylor-series-based methods can significantly overperform the state-of-the-art solvers.