Differential equations

The use of systems of differential equations in mathematical modelling in conjunction with epidemiology continues to be an area of focused research. Chapter one briefly acquaints readers with epidemiology, cholera, and the need for effective control strategies. Chapter two of th…

This thesis explores several models in continuum mechanics from both local and nonlocal perspectives. The first portion settles a conjecture proposed by Filippo Gazzola and his collaborators on the finite-time blow-up for a class of fourth-order differential equations modeling s…

A new approach to the numerical solution of boundary value problems for differential equations which originated in recent papers by Greengard and Rokhlin, is improved and adapted to the numerical solution of the radial Schrödinger equation. The approach is based on the conversio…

Ordinary and partial differential equations with impulsive effects describe phenomena in the applied sciences that admit sudden jumps in their states at some time instants called impulse moments. Most often the phenomena under consideration occur on finite time interval. This sh…

Synthetic biology (SB) has become an important field of science focusing on designing and engineering new biological parts and systems, or re-designing existing biological systems for useful purposes. The dramatic growth of SB throughout the past two decades has not only provide…