TY - BOOK ID - 7198243 TI - Numerical solution of time-dependent advection-diffusion-reaction equations AU - Hundsdorfer, Willem H. AU - Verwer, Jan G. PY - 2010 VL - 33 SN - 01793632 SN - 9783642057076 3540034404 9783540034407 3642057071 3662090171 PB - Berlin: Springer, DB - UniCat KW - Differential equations KW - Differential equations, Partial KW - Stiff computation (Differential equations) KW - Runge-Kutta formulas KW - Numerical solutions KW - -Differential equations, Partial KW - -Stiff computation (Differential equations) KW - Runge-Kutta methods KW - Computation, Stiff (Differential equations) KW - Equations, Stiff (Differential equations) KW - Stiff equations (Differential equations) KW - Stiff systems (Differential equations) KW - Systems, Stiff (Differential equations) KW - Runge-Kutta formulas. KW - Stiff computation (Differential equations). KW - 519.63 KW - 519.63 Numerical methods for solution of partial differential equations KW - Numerical methods for solution of partial differential equations KW - 517.91 Differential equations KW - Partial differential equations KW - Numerical solutions of differential equations KW - 517.91 KW - Numerical solutions. KW - Applied mathematics. KW - Engineering mathematics. KW - Partial differential equations. KW - Differential equations. KW - Numerical analysis. KW - Mathematical and Computational Engineering. KW - Partial Differential Equations. KW - Ordinary Differential Equations. KW - Numerical Analysis. KW - Mathematical analysis KW - Engineering KW - Engineering analysis KW - Mathematics KW - Numerical solutions&delete& KW - Numerical analysis KW - Differential equations - Numerical solutions KW - Differential equations, Partial - Numerical solutions UR - https://www.unicat.be/uniCat?func=search&query=sysid:7198243 AB - "This book describes numerical methods for partial differential equations (PDEs) coupling advection, diffusion and reaction terms, encompassing methods for hyperbolic, parabolic and stiff and nonstiff ordinary differential equations (ODEs). The emphasis lies on time-dependent transport-chemistry problems, describing e.g. the evolution of concentrations in environmental and biological applications. Along with the common topics of stability and convergence, much attention is paid on how to prevent spurious, negative concentrations and oscillations, both in space and time. Many of the theoretical aspects are illustrated by numerical experiments on models from biology, chemistry and physics. A unified approach is followed by emphasizing the method of lines or semi-discretization. In this regard this book differs substantially from more specialized textbooks which deal exclusively with either PDEs or ODEs. This book treats integration methods suitable for both classes of problems and thus is of interest to PDE researchers unfamiliar with advanced numerical ODE methods, as well as to ODE researchers unaware of the vast amount of interesting results on numerical PDEs". -- Cover. ER -