Includes bibliographical references.

Continuous extension of the discrete cosine transform, and its applications to data processing ; Symbolic algorithms for the Painleve test, special solutions, and recursion operators for nonlinear PDEs ; Continuum limit of lattice approximation schemes ; Algebraic structures on ordered rooted trees and their significance to Lie group integrators ; Aspects of generalized double-bracket flows ; Eulerian and semi-Lagrangian schemes based on commutator-free exponential integrators ; Second order linear ODEs: Two non-Liouvillian approaches ; On rational solutions of the fourth Painleve equation and its Hamiltonian ; Comparison of symmetry preserving difference schemes with standard numerical methods ; Symbolic computation of polynomial conserved densities, generalized symmetries, and recursion operators for nonlinear differential-difference equations ; On the numerical analysis of rapid oscillation ; On conservation properties of semidiscrete canonical Hamiltonian equations ; Discrete Lie symmetries for difference equations ; Trivializations, factorizations, and geometric integration for pseudo-rigid bodies ; Towards a variational complex for the finite element method ; Models of resonantly driven motion of motor proteins in 2D potentials ; Determination of approximate symmetries of differential equations ; Discrete and finite fractional Fourier transform ; Some nanotube-like systems and their discrete equations ; Explicit multipoint rational interpolation Pade table for exponential and power functions