2020/01/30 by Emmanuel Asante-Asamani, E.O. Asante-Asamani, E. O. Asante-Asamani +5 · 19 citations
Computer Science · Engineering · Mathematics · #Applied mathematics #Boundary (topology) #Boundary value problem #Computer science #Differential Equations and Numerical Methods #Diffusion #Dirichlet boundary condition #Dirichlet distribution #Electromagnetic Simulation and Numerical Methods #Exponential function #Exponential growth #Linear system #Mathematical analysis #Mathematics #Numerical methods for differential equations #Order (exchange) #Physics #Pure mathematics #Reaction–diffusion system #Scheme (mathematics) #Variety (cybernetics) #Von Neumann architecture #cs.NA #math.NA #msc:65F60 #msc:65M12 #msc:65M15 #msc:65M20
paper · pdf · doi:10.1016/j.jcp.2020.109490
published in Journal of Computational Physics 415, 109490 (Elsevier BV) · 28 pages, 9 figures
arxiv created 2020/01/30 · openalex created_date 2020/02/07 · openalex publication_date 2020/04/30 · arxiv updated 2020/06/24 · openalex updated_date 2026/08/05
A second-order L-stable exponential time-differencing (ETD) method is developed by combining an ETD scheme with approximating the matrix exponentials by rational functions having real distinct poles (RDP), together with a dimensional splitting integrating factor technique. A variety of non-linear reaction-diffusion equations in two and three dimensions with either Dirichlet, Neumann, or periodic boundary conditions are solved with this scheme and shown to outperform a variety of other second-order implicit-explicit schemes. An additional performance boost is gained through further use of basic parallelization techniques.