A systematic method for the derivation of high order schemes for affinely controlled nonlinear systems is developed. Using an adaptation of the stochastic Taylor expansion for control systems we construct Taylor schemes of arbitrary high order and indicate how derivative free Runge-Kutta type schemes can be obtained. Furthermore an approximation technique for the multiple control integrals appe...

Type II matrices were introduced in connection with spin models for link invariants. It is known that a pair of Bose-Mesner algebras (called a dual pair) of commutative association schemes are naturally associated with each type II matrix. In this paper, we show that type II matrices whose Bose-Mesner algebras are imprimitive are expressed as so-called generalized tensor products of some type I...

We are interested in a class of numerical schemes for the optimization of nonlinear hyperbolic partial differential equations. We present continuous and discretized relaxation schemes for scalar, one– conservation laws. We present numerical results on tracking type problems with nonsmooth desired states and convergence results for higher– order spatial and temporal discretization schemes.

We considered finite difference methods of higher order for semilinear singularly perturbed boundary value problems, consisted of constructing difference schemes on nonuniform meshes. Construction of schemes is presented and convergence uniform in perturbation parameter for one method is shown on Bakhvalov’s type of mesh. Numerical experiments demonstrated influence of different meshes on devel...

Submitted to the Journal of Computational Physics Seven schemes to maintain the r B = 0 constraint numerically are compared. All these algorithms can be combined with shock-capturing Godunov type base schemes. They fall into three categories: the eight-wave formulation maintains the constraint to truncation error, the projection scheme enforces the constraint in some discretization by projectin...

With the increasing popularity of XML, there arises the need for managing and querying information in this form. Several query languages, such as XQuery, have been proposed which return their results in document order. However, most recent efforts focused on query optimization have either disregarded order or proposed static schemes in which updates are not handled efficiently. Some dynamic lab...