Computational Methods and Convergence Analyses for First Order Hyperbolic Delay Partial Differential Equations

Abstract

This thesis provides convergent numerical methods for solving first order hyperbolic newlinedelay partial differential equations with initial value problems. Hyperbolic delay partial newlinedifferential equations are commonly encountered in various science and engineering newlineproblems. They play a prominent role in modelling the flow and transport process. newlineThere are many disciplines that benefit from these equations, such as neuroscience, fluid newlinemechanics, gas dynamics, population dynamics, traffic flow, geophysics, meteorology, newlineelectromagnetism, astrophysics, etc. Owing to the numerous applications of these newlineequations, researchers have been paying considerable attention to the development of newlinemethods for obtaining numerical and analytic solutions to linear and non-linear hyperbolic newlinetype partial differential equations. However, numerical methods are more popular in newlinecomparison with analytical methods because of their ease of application, comparatively newlinelesser computational effort and formulation of corresponding computer programs newline