Discrete and Continuous Models and Applied Computational Science最新文献_第7页

Numerical determination of the singularity order of a system of differential equations 微分方程组奇异阶的数值确定

Discrete and Continuous Models and Applied Computational Science Pub Date : 2020-12-15 DOI: 10.22363/2658-4670-2020-28-1-17-34

A. Baddour, M. Malykh, A. A. Panin, L. Sevastianov

{"title":"Numerical determination of the singularity order of a system of differential equations","authors":"A. Baddour, M. Malykh, A. A. Panin, L. Sevastianov","doi":"10.22363/2658-4670-2020-28-1-17-34","DOIUrl":"https://doi.org/10.22363/2658-4670-2020-28-1-17-34","url":null,"abstract":"We consider moving singular points of systems of ordinary differential equations. A review of Painlevé’s results on the algebraicity of these points and their relation to the Marchuk problem of determining the position and order of moving singularities by means of finite difference method is carried out. We present an implementation of a numerical method for solving this problem, proposed by N. N. Kalitkin and A. Al’shina (2005) based on the Rosenbrock complex scheme in the Sage computer algebra system, the package CROS for Sage. The main functions of this package are described and numerical examples of usage are presented for each of them. To verify the method, computer experiments are executed (1) with equations possessing the Painlevé property, for which the orders are expected to be integer; (2) dynamic Calogero system. This system, well-known as a nontrivial example of a completely integrable Hamiltonian system, in the present context is interesting due to the fact that coordinates and momenta are algebraic functions of time, and the orders of moving branching points can be calculated explicitly. Numerical experiments revealed that the applicability conditions of the method require additional stipulations related to the elimination of superconvergence points.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44434370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

On the realization of explicit Runge-Kutta schemes preserving quadratic invariants of dynamical systems 保持动力系统二次不变量的显式龙格-库塔格式的实现

Discrete and Continuous Models and Applied Computational Science Pub Date : 2020-12-15 DOI: 10.22363/2658-4670-2020-28-4-327-345

Yu Ying, Ин Юй, M. Malykh, М Д Малых

{"title":"On the realization of explicit Runge-Kutta schemes preserving quadratic invariants of dynamical systems","authors":"Yu Ying, Ин Юй, M. Malykh, М Д Малых","doi":"10.22363/2658-4670-2020-28-4-327-345","DOIUrl":"https://doi.org/10.22363/2658-4670-2020-28-4-327-345","url":null,"abstract":"We implement several explicit Runge-Kutta schemes that preserve quadratic invariants of autonomous dynamical systems in Sage. In this paper, we want to present our package ex.sage and the results of our numerical experiments. In the package, the functions rrk_solve, idt_solve and project_1 are constructed for the case when only one given quadratic invariant will be exactly preserved. The function phi_solve_1 allows us to preserve two specified quadratic invariants simultaneously. To solve the equations with respect to parameters determined by the conservation law we use the elimination technique based on Grbner basis implemented in Sage. An elliptic oscillator is used as a test example of the presented package. This dynamical system has two quadratic invariants. Numerical results of the comparing of standard explicit Runge-Kutta method RK(4,4) with rrk_solve are presented. In addition, for the functions rrk_solve and idt_solve, that preserve only one given invariant, we investigated the change of the second quadratic invariant of the elliptic oscillator. In conclusion, the drawbacks of using these schemes are discussed.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45620224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Numerical modeling of laser ablation of materials 激光烧蚀材料的数值模拟

Discrete and Continuous Models and Applied Computational Science Pub Date : 2020-12-15 DOI: 10.22363/2658-4670-2020-28-4-398-405

I. Amirkhanov, N. Sarker, I. Sarkhadov

引用次数: 0

Single-mode propagation of adiabatic guided modes in smoothly irregular integral optical waveguides 光滑不规则积分光波导中绝热导模的单模传播

Discrete and Continuous Models and Applied Computational Science Pub Date : 2020-12-15 DOI: 10.22363/2658-4670-2020-28-4-361-377

A. Sevastianov

{"title":"Single-mode propagation of adiabatic guided modes in smoothly irregular integral optical waveguides","authors":"A. Sevastianov","doi":"10.22363/2658-4670-2020-28-4-361-377","DOIUrl":"https://doi.org/10.22363/2658-4670-2020-28-4-361-377","url":null,"abstract":"This paper investigates the waveguide propagation of polarized electromagnetic radiation in a thin-film integral optical waveguide. To describe this propagation, the adiabatic approximation of solutions of Maxwells equations is used. The construction of a reduced model for adiabatic waveguide modes that retains all the properties of the corresponding approximate solutions of the Maxwell system of equations was carried out by the author in a previous publication in DCM ACS, 2020, No 3. In this work, for a special case when the geometry of the waveguide and the electromagnetic field are invariant in the transverse direction. In this case, there are separate nontrivial TEand TM-polarized solutions of this reduced model. The paper describes the parametrically dependent on longitudinal coordinates solutions of problems for eigenvalues and eigenfunctions - adiabatic waveguide TE and TM polarizations. In this work, we present a statement of the problem of finding solutions to the model of adiabatic waveguide modes that describe the stationary propagation of electromagnetic radiation. The paper presents solutions for the single-mode propagation of TE and TM polarized adiabatic waveguide waves.","PeriodicalId":34192,"journal":{"name":"Discrete and Continuous Models and Applied Computational Science","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47576594","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 2

Stochastic analysis of a single server unreliable queue with balking and general retrial time 具有阻塞和一般重试时间的单服务器不可靠队列的随机分析

Discrete and Continuous Models and Applied Computational Science Pub Date : 2020-12-15 DOI: 10.22363/2658-4670-2020-28-4-319-326

Mohamed Boualem

引用次数: 4

Investigation of insertion tableau evolution in the Robinson-Schensted-Knuth correspondence Robinson-Schensted-Knuth对应中插入表演化的研究

Discrete and Continuous Models and Applied Computational Science Pub Date : 2019-12-15 DOI: 10.22363/2658-4670-2019-27-4-316-324

V. Duzhin, В С Дужин

引用次数: 3