Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the development and application of the Fourier method to the numerical solution of Ito stochastic differential equations. Fourier series are widely used in various fields of applied mathematics and physics. However, the method of Fourier series as applied to the numerical solution of stochastic differential equation...

Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis paper is devoted to the comparative analysis of the efficiency of using the Legendre polynomials and trigonometric functions for the numerical solution of Ito stochastic differential equations under the method of approximating multiple Ito and Stratonovich stochastic integrals based on generalized multiple Fourier series. Using the mul...

Kuznetsov, D. F.
Published in
Computational Mathematics and Mathematical Physics

AbstractA strongly converging method of order 2.5 for Ito stochastic differential equations with multidimensional nonadditive noise based on the unified Taylor–Stratonovich expansion is proposed. The focus is on the approaches and methods of mean square approximation of iterated Stratonovich stochastic integrals of multiplicities 1–5 the numerical ...

Biswas, Anjan Sonmezoglu, Abdullah Ekici, Mehmet Kara, Abdul Hamid Alzahrani, Abdullah Kamis Belic, Milivoj R.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis work studies cubic–quartic optical solitons with Kudryashov’s law of refractive index. The extended trial function approach reveals solutions to the model in terms of Jacobi’s elliptic functions that yields bright and singular optical solitons with limiting values to the modulus of ellipticity. The conservation laws are also presented....

Izadi, M. Yüzbaşı, Ş. Adel, W.
Published in
Computational Mathematics and Mathematical Physics

AbstractThis study is concerned with the numerical solutions of the squeezing flow problem which corresponds to fourth-order nonlinear equivalent ordinary differential equations with boundary conditions. We have two goals to obtain numerical solutions to the problem in this paper. One of them is to obtain numerical solutions based on the Bessel pol...

Zaborskii, A. V. Nesterov, A. V. Nechaev, D. Yu.
Published in
Computational Mathematics and Mathematical Physics

AbstractA formal asymptotic expansion of the solution to the Cauchy problem for a singularly perturbed operator differential transport equation in several space variables with weak nonlinearity is constructed. Under certain conditions imposed on the data of the problem, the asymptotic expansion is constructed in the form of series in powers of a sm...

Kokurin, M. M.
Published in
Computational Mathematics and Mathematical Physics

AbstractA class of iteratively regularized Gauss–Newton methods for solving irregular nonlinear equations with smooth operators in a Hilbert space is investigated. The iteration stopping rule is an a posteriori one similar to V.A. Morozov’s discrepancy principle. The regularizing property of the iterations is established, and an accuracy estimate f...

Repin, S. I.
Published in
Computational Mathematics and Mathematical Physics

AbstractFor elliptic equations of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Lambda {\text{*}}\mathcal{A}\Lambda u + \ell = 0$$\end{document}, we examine...

Ajeel, M. Shareef Gachpazan, M. Soheili, Ali R.
Published in
Computational Mathematics and Mathematical Physics

AbstractIn this paper, we present a numerical method for solving a class of nonlinear fractional partial differential equations (FPDEs). The method consists of expanding the required approximate solution as the elements of Sinc functions along the space direction and fractional Muntz–Legendre polynomials for the time variable. By using these functi...

Blatov, I. A. Zadorin, A. I. Kitaeva, E. V.
Published in
Computational Mathematics and Mathematical Physics

AbstractThe problem of cubic spline interpolation on Bakhvalov meshes for functions with high gradients is considered. Error estimates are obtained in the class of functions with high gradients in an exponential boundary layer. According to these estimates, the error of a spline can increase indefinitely as a small parameter tends to zero for a fix...