We show that the well-known order reduction phenomenon affecting implicit Runge-Kutta methods does not occur when approximating periodic solutions of the Korteweg-de Vries equation.

This survey gives an overview of several fundamental algebraic constructions which arise in the study of splines. Splines play a key role in approximation theory, geometric modeling, and numerical analysis; their properties depend on combinatorics, topology, and geometry of a simplicial or polyhedral subdivision of a region in Rk, and are often quite subtle. We describe four algebraic technique...

Let ρ be an unknown Borel measure defined on the space Z := X × Y with X ⊂ IR and Y = [−M,M ]. Given a set z ofm samples zi = (xi, yi) drawn according to ρ, the problem of estimating a regression function fρ using these samples is considered. The main focus is to understand what is the rate of approximation, measured either in expectation or probability, that can be obtained under a given prior...

1 Time-dependent perturbation theory 1 1.1 Rotating frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Perturbation expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 NMR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Periodic perturbations . . . . . . . . . . . . . . . . . ....

first riccati equation with matrix variable coefficients, arising in optimal and robust control approach, is considered. an analytical approximation of the solution of nonlinear differential riccati equation is investigated using the adomian decomposition method. an application in optimal control is presented. the solution in different order of approximations and different methods of approximat...