检索结果-内蒙古大学图书馆

Numerical solution of nonlinear partial quadratic integro-differential equations of fractional order via hybrid of block-pulse and parabolic functions

引用

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS 2019年第3期35卷 1134-1151页

作者： Mirzaee, Farshid Alipour, Sahar Malayer Univ Fac Math Sci & Stat POB 65719-95863 Malayer Iran

In this paper, an effective numerical approach based on a new two-dimensional hybrid of parabolic and block-pulse functions (2D-PBPFs) is presented for solving nonlinear partial quadratic integro-differential equations of fractional order. Our approach is based on 2D-PBPFs operational matrix method together with the fractional integral operator, described in the Riemann-Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations, which greatly simplifies the problem. By using Newton's iterative method, this system is solved, and the solution of fractional nonlinear partial quadratic integro-differential equations is achieved. Convergence analysis and an error estimate associated with the proposed method is obtained, and it is proved that the numerical convergence order of the suggested numerical method is O(h(3)). The validity and applicability of the method are demonstrated by solving three numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the exact solutions much easier.

关键词： block-pulse functions fractional calculus nonlinear quadratic integral equation operational matrix parabolic functions partial differential equation

来源：评论

学校读者我要写书评

暂无评论

Numerical solution based on hybrid of block-pulse and parabolic functions for solving a system of nonlinear stochastic It(o)over-cap-Volterra integral equations of fractional order

引用

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2019年 349卷 157-171页

作者： Mirzaee, Farshid Alipour, Sahar Samadyar, Nasrin Malayer Univ Fac Math Sci & Stat POB 65719-95863 Malayer Iran

In this study, an effective numerical approach based on the hybrid of block-pulse and parabolic functions (PBPFs) is suggested to obtain an approximate solution of a system of nonlinear stochastic It (o) over cap -Volterra integral equations of fractional order. For this aim, we first introduce these functions and express some of their properties and then calculate fractional and stochastic operational matrices of integration based on these functions. Using the properties of PBPFs and obtained operational matrices, the system of nonlinear stochastic It (o) over cap -Volterra integral equations of fractional order converts to a nonlinear system of algebraic equations which can be easily solved by using Newton's method. Moreover, in order to show the rate of convergence of the suggested approach, we present several theorems on convergence analysis and error estimation which demonstrate the rate of convergence of the proposed method for solving this nonlinear system is O(h(3)). Finally, two examples are included to illustrate the validity, applicability and efficiency of the proposed technique. (C) 2018 Elsevier B.V. All rights reserved.

关键词： parabolic functions Block-pulse functions Stochastic integral equations Brownian motion process Fractional calculus Operational matrix

来源：评论

学校读者我要写书评

暂无评论

Characterization of finite shift via Herglotz's representation

引用

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2025年第1期542卷

作者： Cruz-Zamorano, Francisco J. Univ Seville Escuela Tecn Super Ingn Dept Matemat Aplicada 2 Camino Descubrimientos s-n Seville 41092 Spain Univ Seville Escuela Tecn Super Ingn IMUS Camino Descubrimientos s-n Seville 41092 Spain

A complete characterization of parabolic self-maps of finite shift is given in terms their Herglotz's representation. This improves a previous result due to Contreras, Diaz-Madrigal, and Pommerenke. We also derive some consequences for the rate of convergence of these functions to their Denjoy-Wolff point, improving a related result of Kourou, Theodosiadis, and Zarvalis for the continuous setting. (c) 2024 The Author. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

关键词： parabolic functions Complex iteration Finite shift Rate of convergence

来源：评论

学校读者我要写书评

暂无评论

A Hybrid Approach of Nonlinear Partial Mixed Integro-Differential Equations of Fractional Order

引用

IRANIAN JOURNAL OF SCIENCE AND TECHNOLOGY TRANSACTION A-SCIENCE 2020年第3期44卷 725-737页

作者： Mirzaee, Farshid Alipour, Sahar Malayer Univ Fac Math Sci & Stat POB 65719-95863 Malayer Iran

In this paper, we use hybrid parabolic and block-pulse functions (2D-PBPFs) to provide an approximate solution of nonlinear partial mixed Volterra-Fredholm integro-differential equations of fractional order. To reach this goal, we present the Volterra integral operational matrix, operational matrix of fractional integral and operational matrix of mixed VolterraFredholm integral by 2D-PBPFs. Using the proposed method, nonlinear partial mixed Volterra-Fredholm integro-differential equations of fractional order become into a nonlinear system of algebraic equations. Moreover, we provide some theorems for convergence analysis and we demonstrate that the convergence order of the suggested approximate approach is Ooh3THORN. Finally, we solve two numerical examples to prove the accuracy of the proposed method.

关键词： parabolic functions Block-pulse functions Partial differential equation Mixed Volterra-Fredholm integral equation Fractional calculus Operational matrix

来源：评论

学校读者我要写书评

暂无评论

Improving the teaching and learning of parabolic functions by the use of information and communication technology (ICT)

引用

Journal of the Southern African Association for Research in Mathematics, Science and Technology Education 2010年第1期14卷 49-60页

This paper reports a study on the use of ICT to teach parabolic functions to secondary school students. The project was informed by the need to find better ways of presenting parabolic functions to secondary school students in order to improve their learning of the concepts and improve their interest and performance in mathematics. The study was also influenced by the global call for the integration of ICT into teaching and learning, the enormous investments by the South African government and other stakeholders in ICT in education, and the increasing demand for academic excellence in mathematics. In the study, computer graphing software (Graphmatica) was used by students to explore parabolic functions. This paper addresses the questions: Can ICT help students to have a better learning of parabolic functions compared to traditional teaching and learning and how can ICT help students to have a better learning of parabolic functions compared to traditional teaching and learning? The study employed a mixed method research design in the light of a practical action research paradigm. Data was collected from two grade 11 mathematics classes at a secondary school in the North-West Province of South Africa using teaching and learning documents (students' assignments and test scripts), classroom observation and formal/informal interviews. Data from students' performances on the assignments and test, classroom observations and interviews were analysed using descriptive narrative. The study found that ICT could help students learn parabolic functions and may also make the lessons enjoyable to students. The findings imply that integrating ICT into the teaching and learning of parabolic functions and perhaps other topics in mathematics will likely help to improve students' attitude towards mathematics and consequently improve their performances in this learning area.

关键词： activity theory ICT mathematics parabolic functions

来源：评论

学校读者我要写书评

暂无评论

SECOND ANGULAR DERIVATIVES AND parabolic ITERATION IN THE UNIT DISK

引用

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 2010年第1期362卷 357-388页

作者： Contreras, Manuel D. Diaz-Madrical, Santiago Pommerenke, Christian Univ Seville Dept Matemat Aplicada 2 Escuela Tecn Super Ingn Seville 41092 Spain Tech Univ Berlin Inst Math D-10623 Berlin Germany

In this paper we deal with second angular derivatives at Denjoy-Wolff points for parabolic functions in the unit disc. Namely, we study and analyze the existence and the dynamical meaning of this second angular derivative. For instance, we provide several characterizations of that existence in terms of the so-called Koenigs function. It is worth pointing out that there are two quite different classes of parabolic iteration: those with positive hyperbolic step and those with zero hyperbolic step. In the first case, the Koenigs function is in the Caratheodory class but, in the second case, it is even unknown if it is normal. Therefore, the ideas and techniques to approach these two cases are really different. In the end, we also present several rigidity results related to the second angular derivatives at Denjoy-Wolff points.

关键词： Second angular derivative parabolic functions Denjoy-Wolff point Koenigs function rigidity

来源：评论

学校读者我要写书评

暂无评论

parabolic Harnack inequality for the mixture of Brownian motion and stable process

引用

TOHOKU MATHEMATICAL JOURNAL 2007年第1期59卷 1-19页

作者： Song, Renming Vondracek, Zoran Univ Illinois Dept Math Urbana IL 61801 USA Univ Zagreb Dept Math Zagreb 41000 Croatia

Let X be a mixture of independent Brownian motion and symmetric stable process. In this paper we establish sharp bounds for transition density of X, and prove a parabolic Harnack inequality for nonnegative parabolic f... 详细信息

关键词： parabolic Harnack inequality parabolic functions Brownian motion stable processes transition density

来源：评论

学校读者我要写书评

暂无评论

On minimal parabolic functions and time-homogeneous parabolic h-transforms

引用

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 1999年第9期351卷 3499-3531页

作者： Burdzy, K Salisbury, TS Univ Washington Dept Math Seattle WA 98195 USA York Univ Dept Math & Stat N York ON M3J 1P3 Canada

Does a minimal harmonic function h remain minimal when it is viewed as a parabolic function? The question is answered for a class of long thin semi-infinite tubes D subset of R-d of variable width and minimal harmonic functions h corresponding to the boundary point of D "at infinity." Suppose f(u) is the width of the tube u units away from its endpoint and f is a Lipschitz function. The answer to the question is affirmative if and only if integral(infinity) f(3) (u)du = infinity. If the test fails, there exist parabolic h-transforms of space-time Brownian motion in D with infinite lifetime which are not time-homogenous.

关键词： Martin boundary harmonic functions parabolic functions Brownian motion h-transforms

来源：评论

学校读者我要写书评

暂无评论

SPACE-TIME PROCESSES, parabolic functions AND ONE-DIMENSIONAL DIFFUSIONS

引用

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 1973年第448期175卷 409-438页

作者： LAI, TL COLUMBIA UNIV DEPT MATH STATISTICSNEW YORKNY 10027

Abstract: In this paper, we study the properties of the space-time process and of parabolic functions associated with a Markov process. Making use of these properties and the asymptotic behavior of the first passage probabilities near the boundary points, we prove certain theorems concerning when $u(X(t),t)$ is a martingale, where $X(t)$ is a conservative regular one-dimensional diffusion with inaccessible boundaries. A characterization of the class of parabolic functions associated with classical diffusions is also obtained.

关键词： Space-time processes parabolic functions characteristic operators semigroups infinitesimal generators martingales diffusions inacessible boundaries entrance boundaries natural boundaries scale positive increasing (decreasing) solutions boundary crossing probabilities

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：