Parallel Numeric Solution of Differential Equations

The contribution deals with the parallel numerical solution of the partial differential equations. 

The method of lines is used to transform the original problem into a large system of ordinary differential equations. The resulting system 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.