In this work, we obtain explicit estimates for the accuracy of an approximation solution scheme for ODEs. The scheme is of the fourth order and based on the Taylor formula. Here we derive estimates with explicit constants, which are expressed by the derivatives of the right-hand side.
| Mualliflar | Abdullaev, Abdugani, Azamov, Abdulla, Ruziboev, Marks, Tilavov, Asliddin |
|---|---|
| Jurnal | O‘zbekiston matematika jurnali |
| Nashr sanasi | 2026-07-02 |
| Jild | 70 |
| Son | 2 |
| Betlar | 5-14 |
| Til | Ingliz |
| DOI | 10.29229/uzmj.2026-2-1 |
DOI: 10.29229/uzmj.2026-2-1 · Maqolaning asl sahifasi
Dynamical system, Cauchy problem, approximate solution, Taylor formula, Gronwall’s lemma, solution accuracy, accuracy level, error estimation.
In this paper, a new family of Pauli quaternions whose components are the Gaussian Leonardo numbers is defined. These new Pauli quaternions are called Pauli Gaussian Leonardo quaternions. Furthermore, several properties…
This paper systematically establishes the fundamental geometrical and topological properties of the Minkowski operator on convex sets in an Euclidean space. The convexity, closedness, and boundary properties of the…
The paper considers a mixed problem for a quasilinear system of hyperbolic equations in Riemann invariants with dissipative nonlinear boundary conditions. To numerically solve the mixed problem, an initial-boundary…
It is studied inequalities between three elementary symmetric polynomials being trinomial generalization of the well-known Muirhead's inequality. Some sufficient conditions have been derived. A sufficient and necessary…
In the article, high-accuracy difference schemes for the Cauchy problem for a system of fourth-order equations are obtained. Based on the method of energy inequalities, the stability of the scheme is proved, a priori…
In this paper, we study a simple motion evasion differential game of multiple pursuers andone evader. The control functions of the players are subject to integral constraints, where the energies of theplayers change…
This article addresses the well-posedness of a coefficient inverse problem for the three-dimensional Tricomi equation in a parallelepiped. For this problem with nonlocal boundary conditions in anisotropic Sobolev…
In this article, a system of parabolic equations with nonlinear boundary conditionsis transformed into a system of self-similar (automodel) equations by applying a shapeshifting. Anasymptotics for a compact supporting…
In this paper, we aim to study the Cauchy problem posed for a fractional order equation. General solution of the time-fractional equation is found by the Fourier method. The solution to the given problem is shown to be…
In this article, we consider cohomology groups of maximal solvable Lie algebras. We give necessary and sufficient conditions for cohomological rigidity of certain solvable Lie algebras.