Searcharxiv⌕ Search

arXiv subjects

Denis N. Sidorov

Publications and source records attributed to Denis N. Sidorov.

3 recordsLinked to original sources
arXiv2023

Fuzzy Volterra Integral Equation with Piecewise Continuous Kernel: Theory and Numerical Solution

This study aims to discuss the existence and uniqueness of solution of fuzzy Volterra integral equation with piecewise continuous kernel. Such problems appears in many balance problems for hereditary dynamic systems, e.g. in electric load leveling. The method of successive approximations is applied and the main theorems are proved based on the method. Some examples are discussed and the results are presented for different values of $μ$ by plotting several graphs.

math.GM↗
arXiv2015

On Perturbation Method for the First Kind Equations: Regularization and Application

One of the most common problems of scientific applications is computation of the derivative of a function specified by possibly noisy or imprecise experimental data. Application of conventional techniques for numerically calculating derivatives will amplify the noise making the result useless. We address this typical ill-posed problem by application of perturbation method to linear first kind equations $Ax=f$ with bounded operator $A.$ We assume that we know the operator $\tilde{A}$ and source function $\tilde{f}$ only such as $||\tilde{A} - A||\leq δ_1,$ $||\tilde{f}-f||< δ_2.$ The regularizing equation $\tilde{A}x + B(α)x = \tilde{f}$ possesses the unique solution. Here $α\in S,$ $S$ is assumed to be an open space in $\mathbb{R}^n,$ $0 \in \overline{S},$ $α= α(δ).$ As result of proposed theory, we suggest a novel algorithm providing accurate results even in the presence of a large amount of noise.

math.FA↗