aDepartment of Pure and Applied Mathematics, University of Padova, via Trieste 63, 35121 Padova, Italy
bDepartment of Mathematics Methods and Models for Applied Sciences, University of Padova, Italy
Abstract:
We implement a second-order exponential integrator for semidiscretized advection–diffusion–reaction equations, obtained by coupling exponential-like Euler and Midpoint integrators, and computing the relevant matrix exponentials by polynomial interpolation at Leja points. Numerical tests on 2D models discretized in space by finite differences or finite elements, show that the Leja–Euler–Midpoint (LEM) exponential integrator can be up to 5 times faster than a classical second-order implicit solver.