Computational Mathematics and Mathematical Physics 

About: Computational Mathematics and Mathematical Physics is an academic journal published by MAIK Nauka/Interperiodica. The journal publishes majorly in the area(s): Boundary value problem & Nonlinear system. It has an ISSN identifier of 0965-5425. Over the lifetime, 4106 publications have been published receiving 21756 citations.

The non-Sibsonian interpolation : A new method of interpolation of the values of a function on an arbitrary set of points

Abstract: A new method of first-order interpolation of the values of a function on the set of arbitrary points in a finite-dimensional Euclidean space E that differs from the well-known Sibson method is constructed. A number of the properties of this method are proved, and the results of its application and comparison with the Sibson interpolation and with the interpolation based on the Delaunay triangulation are presented. In contrast to the triangulation method, the interpolation proposed is unique; moreover, it is easier and more efficient than the Sibson interpolation.

The bilinear complexity and practical algorithms for matrix multiplication

Abstract: A method for deriving bilinear algorithms for matrix multiplication is proposed. New estimates for the bilinear complexity of a number of problems of the exact and approximate multiplication of rectangular matrices are obtained. In particular, the estimate for the boundary rank of multiplying 3 × 3 matrices is improved and a practical algorithm for the exact multiplication of square n × n matrices is proposed. The asymptotic arithmetic complexity of this algorithm is O(n2.7743).

Solution to the Boltzmann kinetic equation for high-speed flows

Abstract: The Boltzmann kinetic equation is solved by a finite-difference method on a fixed coordinate-velocity grid. The projection method is applied that was developed previously by the author for evaluating the Boltzmann collision integral. The method ensures that the mass, momentum, and energy conservation laws are strictly satisfied and that the collision integral vanishes in thermodynamic equilibrium. The last property prevents the emergence of the numerical error when the collision integral of the principal part of the solution is evaluated outside Knudsen layers or shock waves, which considerably improves the accuracy and efficiency of the method. The differential part is approximated by a second-order accurate explicit conservative scheme. The resulting system of difference equations is solved by applying symmetric splitting into collision relaxation and free molecular flow. The steady-state solution is found by the relaxation method.