This paper elaborates a new version of extended Kalman filtering (EKF) for state estimation in chemical nonlinear continuous-discrete stochastic systems. Such a state estimation always compounds real measurements of some system's variables (depending on the utilized technology) with computation of remaining (not measurable) parameters by means of appropriate filtering algorithms. Here, we consi...

Stabilization to a trajectory for the monodomain equations, a coupled nonlinear PDE-ODE system, is investigated. The results rely on stabilization of linear first-order in time nonautonomous evolution equations combined with stabilizability results for the linearized monodomain equations and a fixed point argument to treat local stabilizability of the nonlinear system. Numerical experiments for...

The specific objective of this paper is to develop a fully implicit compositional simulator for modeling asphaltene deposition during natural depletion. In this study, a mathematical model for asphaltene deposition modeling is presented followed by the solution approach using the fully implicit scheme. A thermodynamic model for asphaltene precipitation and the numerical methods for performing f...

Based on a group of new Saul’yev type asymmetric difference schemes constructed by author, a high-order, unconditionally stable and parallel alternating segment explicit-implicit method for the numerical solution of the fourth-order heat equation is derived in this paper. The truncation error is fourth-order in space, which is much more accurate than the known alternating segment explicit-impli...

For a first order autonomous ODE, we give a polynomial time algorithm to decide whether it has a polynomial general solution and to compute one if it exists. Experiments show that this algorithm is quite effective in solving ODEs with high degrees and a large number of terms.

<p style='text-indent:20px;'>We are interested in the numerical solution of coupled semilinear partial differential equations (PDEs) two and three dimensions. Under certain assumptions on domain, we take advantage Kronecker structure arising standard space discretizations operators illustrate how resulting system ordinary (ODEs) can be treated directly matrix or tensor form. Moreover, fra...

For the implicit systems of first order ordinary differential equations on the plane there is presented the complete local classification of generic singularities of family of its phase curves up to smooth orbital equivalence. Besides the well known singularities of generic vector fields on the plane and the singularities described by a generic first order implicit differential equations, there...

A new two-step implicit linear Obrechkoff twelfth algebraic order method with vanished phase-lag and its first, second, third and fourth derivatives is constructed in this paper. The purpose of this paper is to develop an efficient algorithm for the approximate solution of the one-dimensional radial Schrodinger equation and related problems. This algorithm belongs in the category of the multist...

Two kinds of well studied dynamical systems are state and time discrete ones (important in Computer Science) and state and time continuous ones (heavily considered in Automatic Control). Whereas in the discrete setting, the analysis of computational power of models has led to well-known hierarchies, the situation is more confused in the continuous case. A possible way to discriminate between th...

The so-called elementary canonical state models of the third-order piecewise-linear (PWL) dynamical systems, as the simplest ODE equivalents of Chua’s equations, are presented. Their mutual relations using the linear topological conjugacy are demonstrated in order to show in detail that Chua’s equations and their canonical ODE equivalents represent various forms of qualitatively equivalent mode...