检索结果-内蒙古大学图书馆

A NOVEL NUMERICAL method FOR SOLVING MODIFIED ATANGANA-BALEANU FRACTIONAL PROBLEMS BASED ON THE operational matrix method

引用

FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY 2025年

作者： Abdelhaq, Lana Syam, Sondos m. Syam, Muhammed i. United Arab Emirates Univ Dept Math Sci Al Ain U Arab Emirates

A novel numerical method for solving modified Atangana-Baleanu fractional problems based on the operational matrix method is presented in this paper. We modify the operational matrix method so that its coefficients can be found in an iterative, direct manner. This avoids solving a large algebraic system, which would be computationally expensive. Several theoretical results are presented, including the existence and uniqueness of the solution for our problem, as well as uniform convergence and error estimates. Examples are provided to demonstrate the efficiency of our numerical approach. Both numerical and theoretical results show that our modified approach works very efficiently. Several applications are discussed.

关键词： MABC Derivative Iterative Approach operational matrix method Caputo Type Fractional Initial Value Problems

来源：评论

学校读者我要写书评

暂无评论

An operational matrix method for solving variable-order fractional biharmonic equation

引用

COMPUTATIONAL & APPLIED MATHEMATICS 2018年第4期37卷 4397-4411页

作者： Heydari, M. H. Avazzadeh, Z. Shiraz Univ Technol Dept Math Shiraz Iran Nanjing Normal Univ Sch Math Sci Nanjing 210023 Jiangsu Peoples R China

In this paper, we focus on the fourth-order biharmonic equation which also has been appeared with fractional derivative order. Then, we generalize the fractional biharmonic equation using the concept of variable-order (V-O) fractional derivative in the type of Caputo namely V-O fractional biharmonic equation (V-OFBE). To establish a method for solving V-OFBE, we firstly derive the operational matrix of V-O fractional derivatives for the shifted second kind Chebyshev polynomials. For obtaining this operational matrix with a general procedure, we implement the analytical form of these polynomials and some properties of the V-O fractional derivatives. This approach reduces the V-OFBE to a system of algebraic equations which considerably decreases the following computations. The applicability and reliability of the proposed method are investigated by solving some test problems. The experimental results show the spectral rate of convergence.

关键词： Variable-order fractional biharmonic equation (V-OFBE) Shifted second kind Chebyshev polynomials operational matrix method operational matrix of variable-order fractional derivative

来源：评论

学校读者我要写书评

暂无评论

Approximate solution of fractional differential equations using Shannon wavelet operational matrix method

引用

INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS 2021年第3期13卷 228-244页

作者： Iqbal, Javid Abass, Rustam Kumar, Puneet BGSB Univ Dept Math Sci Rajouri 185234 J&K India Dronacharya Coll Dept Appl Sci Greater Noida 201308 UP India

Many physical problems are frequently governed by fractional differential equations and obtaining the solution of these equations have been the subject of a lot of investigations in recent years. The aim of this paper is to propose a novel and effective method based on Shannon wavelet operational matrices of fractional-order integration. The theory of Shannon wavelets and its properties are first presented. Block Pulse functions and collocation method are employed to derive a general procedure in constructing these operational matrices. The main peculiarity of the proposed technique is that it condenses the given problem into a system of algebraic equations that can be easily solved by MATLAB package. Furthermore, a designed scheme is applied to numerical examples to analyse its applicability, reliability, and effectiveness.

关键词： Shannon wavelets operational matrix method fractional differential equation numerical computation MATLAB

来源：评论

学校读者我要写书评

暂无评论

Numerical solution of systems of differential equations using operational matrix method with Chebyshev polynomials

引用

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE 2018年第2期12卷 155-162页

作者： Ozturk, Yalcin Mugla Sitki Kocman Univ Ula Ali Kocman Vocat Sch Mugla Turkey

In this study, we introduce an effective and successful numerical algorithm to get numerical solutions of the system of differential equations. The method includes operational matrix method and truncated Chebyshev series which represents an exact solution. The method reduces the given problem to a set of algebraic equations including Chebyshev coefficients. Some numerical examples are given to demonstrate the validity and applicability of the method. In Examples, we give some comparison between present method and other numerical methods. The obtained numerical results reveal that given method very good approximation than other methods. Moreover, the modelling of spreading of a non-fatal disease in a population is numerically solved. All examples run the mathematical programme Maple 13.

关键词： Systems of differential equation series expansions stiff problem operational matrix method disease in a population approximate solution

来源：评论

学校读者我要写书评

暂无评论

An operational matrix method to solve linear Fredholm-Volterra integro-differential equations with piecewise intervals

引用

MATHEMATICAL SCIENCES 2021年第2期15卷 189-197页

作者： Ozturk, Yalcin Gulsu, Mustafa Mugla Sitki Kocman Univ Ula Ali Kocman Vocat Sch Mugla Turkey Mugla Sitki Kocman Univ Fac Sci Mugla Turkey

In recent times, operational matrix methods become overmuch popular. Actually, we have many more operational matrix methods. In this study, a new remodeled method is offered to solve linear Fredholm-Volterra integro-differential equations (FVIDEs) with piecewise intervals using Chebyshev operational matrix method. Using the properties of the Chebyshev polynomials, the Chebyshev operational matrix method is used to reduce FVIDEs into a linear algebraic equations. Some numerical examples are solved to show the accuracy and validity of the proposed method. Moreover, the numerical results are compared with some numerical algorithm.

关键词： Piecewise Fredholm– Volterra equations operational matrix method Chebyshev polynomials

来源：评论

学校读者我要写书评

暂无评论

Numerical solution of two dimensional stochastic Volterra–Fredholm integral equations via operational matrix method based on hat functions

引用

SeMA Journal 2020年第3期77卷 227-241页

作者： Mirzaee, Farshid Samadyar, Nasrin Faculty of Mathematical Sciences and Statistics Malayer University P. O. Box 65719-95863 Malayer Iran

Numerical solution of two-dimensional (2D) stochastic integral equations due to randomness has its own difficulties. For instance, most of them do not have analytical solution or obtaining their analytical solution is very hard. So, one of the essential requirement is presenting an efficient method to approximate the solutions of these equations with proper precision. In this paper, we introduce a numerical technique based on two dimensional modification of hat functions (2D MHFs) to estimate the numerical solution of 2D linear stochastic Volterra–Fredholm integral equations. In this approach, first the mentioned equation is transformed into a linear system of algebraic equations and then this system is solved via a direct or numerical method. Furthermore, it is proved that the order of convergence of the proposed method is O(h³). Finally, accuracy of this scheme is measured by solving two test examples via described technique. © 2020, Sociedad Española de Matemática Aplicada.

关键词： Brownian motion process Error analysis operational matrix method Stochastic integral equations Volterra–Fredholm integral equations

来源：评论

学校读者我要写书评

暂无评论

An operational matrix method for Solving a Class of Nonlinear Volterra Integro-Differential Equations by operational matrix method

引用

International Journal of Applied and Computational Mathematics 2017年第4期3卷 3279-3294页

作者： Öztürk, Yalçın Gülsu, Mustafa Ula Ali KoÇman Vocational School Muğla Sıtkı Koçman University Muğla Turkey Department of Mathematics Faculty of Science Muğla Sıtkı Koçman University Muğla Turkey

In this paper, the improved Chebyshev operational matrix method is proposed to solve a class of nonlinear Volterra integro-differential equation. The main characteristic behind this approach is that it reduces such problems to ones of solving systems of algebraic equations. Some examples are included to demonstrate the validity and applicability of the this techinque. The only a small number of shifted Chebyshev polynomials is needed to obtain a satisfactory result. © 2017, Springer India Pvt. Ltd.

关键词： Approximation method Chebyshev polynomials Nonlinear Volterra integro-differential equations Numerical algorithm operational matrix method

来源：评论

学校读者我要写书评

暂无评论

Numerical solution of high order linear complex differential equations via complex operational matrix method

引用

SeMA Journal 2019年第1期76卷 1-13页

作者： Mirzaee, Farshid Samadyar, Nasrin Alipour, Sahar Faculty of Mathematical Sciences and Statistics Malayer University P. O. Box 65719-95863 Malayer Iran

In this work, a numerical method based on a complex operational matrix is utilized to solve high order linear complex differential equations under mixed initial conditions. For this aim, we introduce orthonormal Bernstein polynomials (OBPs), and we obtain their complex operational matrix of differentiation. The main advantage of the proposed method is that by using this method complex differential equations reduce to a linear system of algebraic equations which can be solved by using an appropriate iterative method. To, some results concerning the error analysis associated with the present method are discussed. Finally, we give some numerical examples to reveal accuracy and efficiency of the proposed method. Also, the numerical results obtained by this method are compared with numerical results achieved from other existing methods. © 2018, Sociedad Española de Matemática Aplicada.

关键词： Complex differential equations Error analysis operational matrix method Orthonormal Bernstein polynomials

来源：评论

学校读者我要写书评

暂无评论

Numerical solution of Riccati equation using operational matrix method with Chebyshev polynomials

引用

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS 2015年第2期8卷 1550020-1-1550020-11页

作者： Ozturk, Yalcin Gulsu, Mustafa Mugla Univ Fac Sci Dept Math Mugla Turkey

In this paper, we present numerical technique for solving the Riccati equation by using operational matrix method with Chebyshev polynomials. The method consists of expanding the required approximate solution as truncated Chebyshev series. Using operational matrix method, we reduce the problem to a set of algebraic equations. Some numerical examples are given to demonstrate the validity and applicability of the method. The method is easy to implement and produces very accurate results.

关键词： Riccati equation nonlinear differential equation operational matrix method Chebyshev polynomial approximate solution

来源：评论

学校读者我要写书评

暂无评论

Numerical solution of Abel equation using operational matrix method with Chebyshev polynomials

引用

ASIAN-EUROPEAN JOURNAL OF MATHEMATICS 2017年第3期10卷 1750053-1-1750053-11页

作者： Ozturk, Yalcin Gulsu, Mustafa Mugla Sitki Kocman Univ Ula Ali Kocman Vocat Sch Mugla Turkey Mugla Sitki Kocman Univ Fac Sci Dept Math Mugla Turkey

In this paper, we present a numerical scheme for solving the Abel equation. The approach is based on the shifted Chebyshev polynomials together with operational method. We reduce the problem to a set of nonlinear algebraic equations using operational matrix method. In addition, convergence analysis of the method is presented. Some numerical examples are given to demonstrate the validity and applicability of the method. The only a small number of Chebyshev polynomials is needed to obtain a satisfactory result.

关键词： Approximation by polynomials physical problem Abel equation nonlinear differential equation operational matrix method Chebyshev polynomial

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：