A Compendium of Partial Differential Equation Models

Abstract

Mathematical modelling of physical and chemical systems is used extensively throughout science, engineering, and applied mathematics. To use mathematical models, one needs solutions to the model equations; this generally requires numerical methods. This book presents numerical methods and associated computer code in Matlab for the solution of a spectrum of models expressed as partial differential equations (PDEs). The authors focus on the method of lines (MOL), a well-established procedure for all major classes of PDEs, where the boundary value partial derivatives are approximated algebraically by finite differences. This reduces the PDEs to ordinary differential equations (ODEs) and makes the computer code easy to understand, implement, and modify. Also, the ODEs (via MOL) can be combined with any other ODEs that are part of the model (so that MOL naturally accommodates ODE/PDE models). This book uniquely includes a detailed line-by-line discussion of computer code related to the associated PDE model.

Estudo do desempenho de reator de leito gotejante aplicado ao processo de hidrodessulfurização do petróleo

“…Nesse sentido, um código computacional foi desenvolvido para solução numérica do modelo TBR no software Matlab com base em códigos apresentados por [22], que estabeleceram procedimentos numéricos envolvendo o método das linhas para resolução de EDPs em linguagem Matlab. As principais características do modelo foram: 100 nós de discretização, que foram requeridos para obter uma precisão razoável; o tempo de integração foi longo o suficiente para atingir as condições de estado estacionário; a função ode15i do Matlab para resolução de EDOs rígidas foi utilizada; e a aplicação da expressão de diferença finita atrasada às derivadas parciais espaciais na direção axial.…”

Tumor Evolution in Space: The Effects of Competition Colonization Tradeoffs on Tumor Invasion Dynamics

“…We analyzed both models through numerical simulations, for which we used the method of lines approach (Schiesser and Griffiths, 2009). We used upwind spatial finite differences for the tactic terms.…”

Observer design for a class of hyperbolic PDE equation based on a Distributed Super Twisting Algorithm

“…There exist a great deal of systems which dynamical behaviour can be modelled by Partial Differential Equations (PDE) [19]. In recent years, this research eld has progressed considerably, as more realistic models have been introduced and investigated in different areas such as thermodynamics, elastic structures, uid dynamics and biological systems, to name only few [7], [11].…”