A compendium of partial differential equation models : method of lines analysis with Matlab / William E. Schiesser, Graham W. Griffiths.

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

An introduction to the method of lines -- A one-dimensional, linear partial differential equation -- Green's function analysis -- Two nonlinear, variable-coeffcient, inhomogeneous partial differential equations -- Euler, Navier Stokes, and Burgers equation -- The cubic Schrödinger equation -- The Korteweg-deVries equation -- The linear wave equation -- Maxwell's equations -- Elliptic partial differential equations: Laplace's equation -- Three-dimensional partial differential equation -- Partial differential equation with a mixed partial derivative -- Simultaneous, nonlinear, two-dimensional partial differential equations in cylindrical coordinates -- Diffusion equation in spherical coordinates -- Appendixes: 1. Partial differential equations from conservation principles: the Anisotropic diffusion equation -- 2. Order conditions for finite-difference approximations -- 3. Analytical solution of nonlinear, traveling wave partial differential equations -- 4. Implementation of time-varying boundary conditions -- 5. The differentiation in space subroutines library -- 6. Animating simulation results.

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.