Task View on Numerical Analysis and Differential Equations

Thu, Mar 8, 2012 6:58 AM

On 08-03-2012, at 12:16, Hans W Borchers wrote:

I am wondering if it would be time to have a new Task View, this time
for the subject of "Numerical Analysis and Differential Equations".
The list of packages possibly appearing in such a task view is already
quite long and could, for example, include:

Numerical Analysis and Linear Algebra

Bessel        Bessel Functions Computations and Approximations
cubature      Adaptive multivariate integration over hypercubes
elliptic      Elliptic and related functions
expm          Matrix exponential, logarithm, etc.
fdim	      Functions for calculating fractal dimension
gaussquad     Collection of functions for Gaussian quadrature
gmp           Multiple precision arithmetic
gsl           Wrapper for the Gnu Scientific Library
hypergeo      The hypergeometric function
irlba         Fast partial SVD by Lanczos bidiagonalization
matlab        MATLAB emulation package
multipol      Multivariate polynomials
numDeriv      Accurate numerical derivatives
onion         Octonions and quaternions
orthogonalsplinebasis  Orthogonal Bspline basis functions
orthopolynom  Functions for orthogonal and orthonormal polynomials
polspline     Polynomial spline routines
polynom       Implement a class for univariate polynomial manipulations
PolynomF      Polynomials in R
pracma        Practical numerical math functions
pspline       Penalized smoothing splines
quaternions   Arithmetics and linear algebra with quaternions
R2Cuba        Multidimensional numerical integration
RcppArmadillo Rcpp integration for Armadillo templated linear algebra library
RcppEigen	  Rcpp integration for the Eigen templated linear algebra library
RcppOctave    Rcpp integration of Octave
R.matlab	  Read and write of MAT files and R-to-Matlab connectivity
Rmpfr	      Multiple precision floating-point reliable
sparseGrid    Sparse grid integration in R
spuRs         Functions and datasets scientific programming and simulation
sspline       Smoothing splines on the sphere
stinepack     Stineman: consistently well behaved method of interpolation
svd           Interfaces to various state-of-art SVD and eigensolvers
voronoi       Methods and applications related to Voronoi tessellations
wavelets...

Simulation and Differential Equations

bvpSolve	  Solvers for boundary value problems of ODEs
ddesolve      Solver for Delay Differential Equations
deSolve       General solvers for initial value problems of ordinary
             differential equations (ODE), partial differential equations
             (PDE), differential algebraic equations (DAE), and delay
             differential equations (DDE)
deTestSet	  Testset for differential equations
odesolve	  Solvers for Ordinary Differential Equations
PBSddesolve	  Solver for Delay Differential Equations
rootSolve     Root finding, equilibrium and steady-state analysis of ODEs
sde           Simulation and Inference for Stochastic Differential Equations
Sim.DiffProc  Simulation of diffusion processes
simecol       Simulation of ecological and other dynamic systems

and probably many more in the end. I left out the optimization
packages deliberately, but of course there would be a strong hint to
that task view.

If you put pracma in "Numerical Analysis and Linear Algebra", then I feel you should also include  BB and nleqslv under that heading. Both of these do things that can be classified as Numerical Analysis. And both can of course also be used for simulation.

BB  solve  (sparse) systems of non linear equations using spectral gradient methods
nleqslv solve systems of nonlinear equations combining global strategies with a Broyden or Newron method.

Berend

Task View on Numerical Analysis and Differential Equations

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