Recent developments in numerical methods and software for ODEs/DAEs/PDEs

Ordinary differential equations (ODEs), differential-algebraic equations (DAEs) and partial differential equations (PDEs) are among the forms of mathematics most widely used in science and engineering. Each of these equation types is a focal point for international collaboration and research. This book contains papers by recognized numerical analysts who have made important contributions to the solution of differential systems in the context of realistic applications, and who now report the latest results of their work in numerical methods and software for ODEs/DAEs/PDEs. The papers address parallelization and vectorization of numerical methods, the numerical solution of ODEs/DAEs/PDEs, and the use of these numerical methods in realistic scientific and engineering applications.

Papers presented at the American Institute of Chemical Enginees Annual Meeting in Chicago, Nov. 11-16, 1990.

An overview of recent developments in numerical methods and software for ODEs/DAEs/PDEs / G.D. Byrne and W.E. Schiesser -- Experiments with an ordinary differential equation solver in the parallel solution of method of lines problems on a shared memory parallel computer / D.K. Kahaner [and others] -- Crayfishpak: a vectorized Fortran package to solve Helmholtz equations / R.A. Sweet -- Experiments with an adaptive H-, P-, and R- refinement finite element method for parabolic systems / J.E. Flaherty and Y. Wang -- Incomplete block factorization preconditioners: an implementation for block tridiagonal systems / D.E. Salane -- Fast generation of weights in finite difference formulas / B. Fornberg -- Numerical methods for boundary value problems in differential-algebraic equations / U.M. Ascher and L.R. Petzold -- The solution of a co-polymerization model with VODE / G.D. Byrne.