Geometric algebra is currently considered as a universal mathematical apparatus of computer graphics. Active research, both academic and applied, is being conducted in this area. …
This paper proposes an original approach to calculating integrals of rapidly oscillating functions, based on Levin’s algorithm, which reduces the search for an anti-derivative …
A numerical algorithm for solving exact differential equations is proposed, based both on the efficient calculation of integrating factors and on a “new” numerical method for …
For describing specialized mathematical structures, it is preferable to use a special formalism rather than a general one. However, tradition often prevails in this case. For …
Tensor formalism (and its special case—vector formalism) is a mathematical technique that is widely used in physical and engineering problems. Even though this formalism is fairy …
Calculations of optical devices in the geometrized Maxwell’s theory use well-known formalisms of general theory of relativity and differential geometry. In particular, for such …
Geometric algebra is based on the works by Grassmann and Clifford. Its main objects of research are polyvectors (p-vectors) and multivectors. Polyvectors, together with the …
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within …
In research problems that involve the use of numerical methods for solving systems of ordinary differential equations (ODEs), it is often required to select the most efficient …
In this paper, two approaches (combinatorial and operatorial) to the stochastization of the one-step processes are discussed for the closed and open version of the Lotka–Volterra …
This paper has a practical aim. For a long time, implementations of pseudorandom number generators in standard libraries of programming languages had poor quality. The situation …
Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is …
The Maxwell equations have a fairly simple form. However, finding solutions of Maxwell's equations is an extremely difficult task. Therefore, various simplifying approaches are …
When the Maxwell equations are geometrized, the Maxwell Lagrangian is usually reduced to the Yang-Mills Lagrangian. In this case, the effective quadratic metric, usually …
The authors for a long time have investigated the phenomenon of global synchronization. Specifically, the occur- rence of a self-oscillatory regime in a control system was …
The most common physical formalisms are the Lagrangian formalism and the Hamiltonian formalism. From the superficial point of view, they are one and the same, but rewritten in …
In this article, we compare the support for SIMD instructions for Julia and Fortran. The comparison is carried out according to the methodology described in work of T. Kalibera, R. …
In certain scientific domains, there is a need for tensor operations. To facilitate tensor computations, computer algebra systems are employed. In our research, we have been using …