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"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.

Differential equations --- Differential equations, Partial --- Stiff computation (Differential equations) --- Runge-Kutta formulas --- Numerical solutions --- -Differential equations, Partial --- -Stiff computation (Differential equations) --- Runge-Kutta methods --- Computation, Stiff (Differential equations) --- Equations, Stiff (Differential equations) --- Stiff equations (Differential equations) --- Stiff systems (Differential equations) --- Systems, Stiff (Differential equations) --- Runge-Kutta formulas. --- Stiff computation (Differential equations). --- 519.63 --- 519.63 Numerical methods for solution of partial differential equations --- Numerical methods for solution of partial differential equations --- 517.91 Differential equations --- Partial differential equations --- Numerical solutions of differential equations --- 517.91 --- Numerical solutions. --- Applied mathematics. --- Engineering mathematics. --- Partial differential equations. --- Differential equations. --- Numerical analysis. --- Mathematical and Computational Engineering. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Numerical Analysis. --- Mathematical analysis --- Engineering --- Engineering analysis --- Mathematics --- Numerical solutions&delete& --- Numerical analysis --- Differential equations - Numerical solutions --- Differential equations, Partial - Numerical solutions