Adaptive Interpolation Algorithm Based on a kd-Tree for Numerical Integration of Systems of Ordinary Differential Equations with Interval Initial Conditions

We consider issues related to the numerical solution of interval systems of ordinary differential equations. We suggest an algorithm that permits finding interval estimates of solutions with prescribed accuracy in reasonable time. The algorithm constructs an adaptive partition (a dynamic structured grid) based on a kd-tree over the space formed by interval initial conditions for the ordinary differential equations. In the operation of the algorithm, a piecewise polynomial function interpolating the dependence of the solution on the specific values of interval parameters is constructed at each step of solution of the original problem. We prove that the global error estimate linearly depends on the height of the kd-tree. The algorithm is tested on several examples; the test results show its efficiency when solving problems of the class under study.     

Wave Mixing in a System of Mobile Coaxial Cylinders

Doklady Physics - Computer simulation of mixing in a system of mobile coaxial cylinders has been performed. Detailed spatial and temporal patterns of the processes occurring are obtained, and the...     

Conjugate model for heat and mass transfer of porous wall in the high temperature gas flow

Heat and mass transfer of a porous permeable wall in a high temperature gas dynamical flow is considered. Numerical simulation is conducted on the ground of the conjugate mathematical model which includes filtration and heat transfer equations in a porous body and boundary layer equations on its surface. Such an approach enables one to take into account complex interaction between heat and mass transfer in the gasdynamical flow and in the structure subjected to this flow. The main attention is given to the impact of the intraporous heat transfer intensity on the transpiration cooling efficiency. The project supported by the National Natural Science Foundation of China (19889209) and Russian Foundation for Basic Research (97-02-16943)     

Numerical simulation of the distribution of charge carrier in nanosized semiconductor heterostructures with account for polarization effects

A three-level scheme for modeling nanosized semiconductor heterostructures with account for spontaneous and piezoelectric polarization effects is presented. The scheme combines quantummechanical calculations at the atomic level for obtaining the charge density on heterointerfaces, calculation of the distribution of carriers in the heterostructure based on the solution to the Schrödinger and Poisson equations, and the calculation of electron mobility in the two-dimensional electron gas with account for various scattering mechanisms. To speed up the computations of electron density in the heterostructure, the approach based on the approximation of the nonlinear dependence of the electron density on the potential in combination with the linearization of the Poisson equation is used. The efficiency of this approach in problems of the class in question is demonstrated.     

Interval Approach to Solving Parametric Identification Problems for Dynamical Systems

Differential Equations - We present an approach to solving parametric identification problems for dynamical systems. The approach is aimed at finding an interval estimate of the model parameters in...     

Adaptive Interpolation Algorithm on Sparse Meshes for Numerical Integration of Systems of Ordinary Differential Equations with Interval Uncertainties

Differential Equations - We consider the theoretical aspects of generalization of the adaptive interpolation algorithm to the case of a large number of interval uncertainties with the use of sparse...