Catálogo de publicaciones - libros

The numerical method we consider is based on the nonstaggered central scheme proposed by Jiang, Levy, Lin, Osher, and Tadmor (SIAM J. Numer. Anal. 35, 2147(1998)) that was obtained by conversion of the standard central NT scheme to the nonstaggered mesh. The generalization we propose is connected with the numerical evaluation of the geometrical source term. The presented scheme is applied to the nonhomogeneous shallow water system. Including an appropriate numerical treatment for the source term evaluation we obtain the scheme that preserves quiescent steady-state for the shallow water equations exactly. We consider two different approaches that depend on the discretization of the riverbed bottom. The obtained schemes are well balanced and present accurate and robust results in both steady and unsteady flow simulations.

A multiple alignment algorithm for protein sequences is considered. Alignment is obtained from a hidden Markov model of the family, which is built using simulated annealing variant of the EM algorithm. Several methods for obtaining the optimal model/alignment are discussed and applied to a family of globins.

In numerical approximation for stochastic ordinary differential equations (SODEs) the main concepts such as relationship between local errors and strong consistency are considered. The main result that consistency conditions given in [P. Kloeden and E. Platen, Numerical Solution of Stochastic Ordinary Differential Equations, Springer-Verlag, 1992] and local errors are equivalent under appropriate conditions.

In this paper a problem of determining the dimension of the bivariate spline space (Δ) is studied. Under certain assumptions on the degrees of vertices and on the collinearity of edges, it is shown that the dimension of the spline space is equal to the lower bound, established by Schumaker in [7].

In this paper we consider the parameter estimation (PE) problem for the logistic function-model in case when it is not possible to measure its values. We show that the PE problem for the logistic function can be reduced to the PE problem for its derivative known as the Hubbert function. Our proposed method is based on finite differences and the total least squares method.

Given the data (, t, y), = 1, …, > 3, we give necessary and sufficient conditions which guarantee the existence of the total least squares estimate of parameters for the Hubbert function, suggest a choice of a good initial approximation and give some numerical examples.

When highly viscous oil is produced at low temperatures, large pressure drops will significantly decrease production rate. One of possible solutions to this problem is heating of oil well by hot water recycling. We construct and analyze a mathematical model of oil-well heating composed of three linear parabolic PDE coupled with one Volterra integral equation. Further on we construct numerical method for the model and present some simulation results.

In this paper, the problem of geometric interpolation of space data is considered. Cubic polynomial parametric curve is supposed to interpolate five points in three dimensional space. It is a case of a more general problem, i.e., the conjecture about the number of points in which can be interpolated by parametric polynomial curve of degree . The necessary and sufficient conditions are found which assure the existence and the uniqueness of the interpolating polynomial curve.

An initial-boundary value problem for one-dimensional flow of a compressible viscous heat-conducting micropolar fluid is considered. It is assumed that the fluid is thermodynamically perfect and polytropic. This problem has a unique strong solution on ]0, 1[×]0, [, for each > 0 ([7]). We also have some estimations of the solution independent of ([8]). Using these results we prove a stabilization of the solution.

The paper presents some results on the existence and behaviour of some parameter classes of solutions for system of quasilinear differential equations. The behaviour of integral curves in neighbourhoods of an arbitrary curve is considered. The obtained results contain the answer to the question on stability as well as approximation of solutions whose existence is established. The errors of the approximation are defined by the functions that can be sufficiently small. The theory of qualitative analysis of differential equations and topological retraction method are used.

We prove a well known formula for the generalized derivatives of Chebyshev B-splines: where in a purely algebraic fashion, and thus show that it holds for the most general spaces of splines. The integration is performed with respect to a certain measure associated in a natural way to the underlying Chebyshev system of functions. Next, we discuss the implications of the formula for some special spline spaces, with an emphasis on those that are not associated with ECC-systems.