2017/02/08 by Jochen Schütz, Schütz, Jochen, David C. Seal +3
Engineering · Mathematics · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1702.02605
openalex publication_date 2017/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we construct novel discretizations for the unsteady\nconvection-diffusion equation. Our discretization relies on multiderivative\ntime integrators together with a novel discretization that reduces the total\nnumber of unknowns for the solver. These type of temporal discretizations come\nfrom an umbrella class of methods that include Lax-Wendroff (Taylor) as well as\nRunge-Kutta methods as special cases. We include two-point collocation methods\nwith multiple time derivatives as well as a sixth-order fully implicit\ncollocation method that only requires a total of three stages. Numerical\nresults for a number of sample linear problems indicate the expected order of\naccuracy and indicate we can take arbitrarily large time steps.\n