Dr. Lisa Davis (Dept. of Mathematical Sciences, MSU) 

9/1/2022  3:10pm

Abstract:

The focus of this talk is the development and analysis of a time filtering process for a compartment model of the transcription of ribosomal RNA in bacteria.  The biological system is described, and then a computational framework for the compartment model simulation is discussed.  We demonstrate that combining a time filter with the classical upwind scheme is an efficient explicit scheme for hyperbolic problems.  The analysis shows that the filtering technique increases accuracy with a minimal computational cost.  The new explicit implementation is presented, and the analysis demonstrates that one can decrease both the local truncation of the scheme as well as its dissipation by adjusting a filter parameter within the algorithm.  The CFL condition for the filtered algorithm is derived using two different methods of stability analysis.  The increased accuracy and decreased dissipation are observed for a set of test problems that are inspired by the biological application.   Numerical computations illustrate stability and convergence as well as dissipation and dispersion assessments of the filtered upwind schemes.