Recent Developments in Numerical Methods and Software for ODEs/DAEs/PDEsOrdinary 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. |
Contents
Preface | 1 |
Shared Memory Parallel Computer | 7 |
A Vectorized Fortran Package to Solve Helmholtz | 37 |
Experiments with an Adaptive H P and RRefinement Finite | 55 |
An Implementation | 81 |
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Common terms and phrases
Appendix applied band matrix BB BB block tridiagonal boundary conditions boundary value problems BSSOR calculations catalyst co-polymer co-polymerization coefficient column components computed convergence coordinates denotes dense linear algebra dependent variable derivative described differential-algebraic equations dimension dimensionless discretization domain eigenvalues error estimates error tolerance example Figure finite element methods function Gaussian elimination GMRES grid points h-refinement implementation incomplete block factorization initial conditions initial value integration iterative methods Jacobian matrix linear algebra linear systems M₁ mathematical model mesh method of lines mol/cm³ moles monomer NMOL nonzero numerical methods numerical solution obtained ODE solver one-dimensional ordinary differential equation Output point package partial differential equations PDEs performance point in physical polymer polymer granule polynomial preconditioners reaction rate reduced diagonal blocks routine SDRIV3 Section SIAM solve spatial speed Speedup spherical step strategy Table techniques TOUT TOUT triangular factors vector VODE weight