Performance analysis on covid-19 models with discontinuities and efficient defect control for initial value ODE solvers

Abstract

<span>In this thesis, we consider the problems of numerically solving ordinary differ ential equation (ODE) and partial differential equation (PDE) Covid-19 models with discontinuities. We then tackle the issue of computing accurate continu ous solutions to ODE problems through an efficient defect control scheme using multistep interpolants. The defect is the amount by which a continuous approx imate solution fails to satisfy the ODE.</span><br /><span>Using a Covid-19 ODE model with discontinuities and the R, Python, Scilab and Matlab programming environment, we discuss how to handle issues with time- and state-dependent discontinuities. Solving a Covid-19 PDE model with an error control PDE solver with event detection capabilities, BACOLIKR [23], we discuss issues associated with solving PDE models with time- and state dependent discontinuities.</span><br /><span>Using the framework of multistep interpolants (Hermite-Birkhoff interpolants), we derive efficient 4^th, 6^th and 8^th order interpolants that can be used to per form defect control. We investigate several questions with this approach and show how to obtain effective defect controlled continuous approximate solutions to ODEs.</span>