Numerical Analysis of Transport Equations Motivated by Neuroscience

This book provides a unified and accessible introduction to the numerical analysis of the first-order hyperbolic partial differential (transport) equations having point-wise delay as well as advance. For model problem in neuronal transport, which leads to advection equations with point-wise delay, the numerical methods have been derived and analyzed. Finite difference and finite volume approaches are used to develop the numerical techniques. Analysis is performed for the mathematical properties of the numerical approximations like estimates for stability and convergence. This book is developed as the result of the doctoral thesis of the author. The book is intended for a wide audience, and will be of great use both to numerical analysis and computational researcher in a variety of applications.