Parallel solution of parabolic partial differential equation using higher-order method

The article focuses on the parallel numerical solution of parabolic partial differential equation. The method of lines is used for the discretization of the problem, which leads to the large system of ordinary differential equations. The resulting system of ordinary differential equations is solved by higher-order numerical method based on 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.