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An Extended Numerical Method by Stancu Polynomials for Solution of Integro-Differential Equations Arising in Oscillating Magnetic Fields
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作者 Neşe İşler Acar 《Advances in Pure Mathematics》 2024年第10期785-796,共12页
In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled b... In this study, the Bernstein collocation method has been expanded to Stancu collocation method for numerical solution of the charged particle motion for certain configurations of oscillating magnetic fields modelled by a class of linear integro-differential equations. As the method has been improved, the Stancu polynomials that are generalization of the Bernstein polynomials have been used. The method has been tested on a physical problem how the method can be applied. Moreover, numerical results of the method have been compared with the numerical results of the other methods to indicate the efficiency of the method. 展开更多
关键词 Stancu Polynomials Collocation Method integro-differential equations Linear equation Systems Matrix equations
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Galerkin Method for Numerical Solution of Volterra Integro-Differential Equations with Certain Orthogonal Basis Function
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作者 Omotayo Adebayo Taiwo Liman Kibokun Alhassan +1 位作者 Olutunde Samuel Odetunde Olatayo Olusegun Alabi 《International Journal of Modern Nonlinear Theory and Application》 2023年第2期68-80,共13页
This paper concerns the implementation of the orthogonal polynomials using the Galerkin method for solving Volterra integro-differential and Fredholm integro-differential equations. The constructed orthogonal polynomi... This paper concerns the implementation of the orthogonal polynomials using the Galerkin method for solving Volterra integro-differential and Fredholm integro-differential equations. The constructed orthogonal polynomials are used as basis functions in the assumed solution employed. Numerical examples for some selected problems are provided and the results obtained show that the Galerkin method with orthogonal polynomials as basis functions performed creditably well in terms of absolute errors obtained. 展开更多
关键词 Galerkin Method integro-differential equation Orthogonal Polynomials Basis Function Approximate Solution
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CONVERGENCE ANALYSIS OF THE JACOBI SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS 被引量:9
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作者 杨银 陈艳萍 黄云清 《Acta Mathematica Scientia》 SCIE CSCD 2014年第3期673-690,共18页
We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorou... We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of Volterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L^∞ norm and weighted L^2-norm. The numerical examples are given to illustrate the theoretical results. 展开更多
关键词 Spectral Jacobi-collocation method fractional order integro-differential equations Caputo derivative
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A lumped mass nonconforming finite element method for nonlinear parabolic integro-differential equations on anisotropic meshes 被引量:6
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作者 SHI Dong-yang WANG Hui-min LI Zhi-yan Dept. of Math., Zhengzhou Univ., Zhengzhou 450052, China 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2009年第1期97-104,共8页
A lumped mass approximation scheme of a low order Crouzeix-Raviart type noncon- forming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is d... A lumped mass approximation scheme of a low order Crouzeix-Raviart type noncon- forming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection. 展开更多
关键词 nonlinear parabolic integro-differential equation nonconforming finite element anisotropic mesh lumped mass error estimate
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MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SINGULAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE 被引量:7
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作者 郭大钧 《Acta Mathematica Scientia》 SCIE CSCD 2012年第6期2176-2190,共15页
In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point ... In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive singular integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type. 展开更多
关键词 impulsive singular integro-differential equation infinite boundary valueproblem fixed point theorem of cone expansion and compression with normtype
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Highly efficient H^1-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation 被引量:7
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作者 石东洋 廖歆 唐启立 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2014年第7期897-912,共16页
A highly efficient H1-Galerkin mixed finite element method (MFEM) is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation ... A highly efficient H1-Galerkin mixed finite element method (MFEM) is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O(h^2) for both the original variable u in H1 (Ω) norm and the flux p = u in H(div, Ω) norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O(h^3) are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method. 展开更多
关键词 parabolic integro-differential equation H1-Galerkin mixed finite elementmethod (MFEM) linear triangular element asymptotic expansion superconvergence andextrapolation
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ON MONOTONE ITERATIVE METHOD FOR INITIAL VALUE PROBLEMS OF NONLINEAR SECOND-ORDER INTEGRO-DIFFERENTIAL EQUATIONS IN BANACH SPACES 被引量:3
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作者 陈芳启 陈予恕 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第5期509-518,共10页
Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differenti... Using the monotone iterative method and Monch Fixed point theorem, the existence of solutions and coupled minimal and maximal quasisolutions of initial value problems for mixed monotone second-order integro-differential equations in Banach spaces are studied. Some existence theorems of solutions and coupled minimal and maximal quasisolutions are obtained. 展开更多
关键词 integro-differential equations Kuratowski measure of noncompactness coupled lower and upper quasisolutions monotone iterative method
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Numerical Methods for a Class of Hybrid Weakly Singular Integro-Differential Equations 被引量:1
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作者 Shihchung Chiang 《Applied Mathematics》 2017年第7期956-966,共11页
This paper proposes numerical methods for solving hybrid weakly singular integro-differential equations of the second kind. The terms in these equations are in the following order: derivative term of a state, integro-... This paper proposes numerical methods for solving hybrid weakly singular integro-differential equations of the second kind. The terms in these equations are in the following order: derivative term of a state, integro-differential term of a state with a weakly singular kernel, a state, integral term of a state with a smooth kernel, and force. The original class of weakly singular integro-differential equations of the first kind is derived from aeroelasticity mathematical models. Among the proposed methods, the method for solving linear cases is fully based on previously reported approximation scheme for equations of the first kind. For nonlinear cases, a revised method is proposed. Examples are presented to demonstrate the effectiveness of the proposed methods, and the results indicate that the proposed methods facilitate achieving satisfactory and accurate approximations. 展开更多
关键词 HYBRID WEAKLY SINGULAR integro-differential equationS
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Existence and Uniqueness of Solution for a Fractional Order Integro-Differential Equation with Non-Local and Global Boundary Conditions 被引量:2
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作者 Mehran Fatemi Nihan Aliev Sedaghat Shahmorad 《Applied Mathematics》 2011年第10期1292-1296,共5页
In this paper, we prove an important existence and uniqueness theorem for a fractional order Fredholm – Volterra integro-differential equation with non-local and global boundary conditions by converting it to the cor... In this paper, we prove an important existence and uniqueness theorem for a fractional order Fredholm – Volterra integro-differential equation with non-local and global boundary conditions by converting it to the corresponding well known Fredholm integral equation of second kind. The considered in this paper has been solved already numerically in [1]. 展开更多
关键词 FRACTIONAL Order integro-differential equation NON-LOCAL BOUNDARY Conditions FUNDAMENTAL Solution
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MULTIPLE POSITIVE SOLUTIONS FOR FIRST ORDER IMPULSIVE SUPERLINEAR INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE 被引量:3
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作者 Guo Dajun 《Acta Mathematica Scientia》 SCIE CSCD 2011年第3期1167-1178,共12页
In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed poi... In this paper, the author discusses the multiple positive solutions for an infinite boundary value problem of first order impulsive superlinear integro-differential equations on the half line by means of the fixed point theorem of cone expansion and compression with norm type. 展开更多
关键词 impulsive superlinear integro-differential equation infinite boundary value problem fixed point theorem of cone expansion and compression with norm type
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Superconvergence of Finite Element Approximations to Parabolic and Hyperbolic Integro-Differential Equations 被引量:2
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作者 张铁 李长军 《Northeastern Mathematical Journal》 CSCD 2001年第3期279-288,共10页
The object of this paper is to investigate the superconvergence properties of finite element approximations to parabolic and hyperbolic integro-differential equations. The quasi projection technique introduced earlier... The object of this paper is to investigate the superconvergence properties of finite element approximations to parabolic and hyperbolic integro-differential equations. The quasi projection technique introduced earlier by Douglas et al. is developed to derive the O(h2r) order knot superconvergence in the case of a single space variable, and to show the optimal order negative norm estimates in the case of several space variables. 展开更多
关键词 SUPERCONVERGENCE parabolic and hyperbolic integro-differential equation finite element
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Solving <i>nth</i>-Order Integro-Differential Equations Using the Combined Laplace Transform-Adomian Decomposition Method 被引量:1
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作者 Waleed Al-Hayani 《Applied Mathematics》 2013年第6期882-886,共5页
In this paper, the Combined Laplace Transform-Adomian Decomposition Method is used to solve nth-order integro-differential equations. The results show that the method is very simple and effective.
关键词 integro-differential equationS LAPLACE Transform METHOD Adomian Decomposition METHOD
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DISCRETE GALERKIN METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS 被引量:1
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作者 P.MOKHTARY 《Acta Mathematica Scientia》 SCIE CSCD 2016年第2期560-578,共19页
In this article, we develop a fully Discrete Galerkin(DG) method for solving ini- tial value fractional integro-differential equations(FIDEs). We consider Generalized Jacobi polynomials(CJPs) with indexes corres... In this article, we develop a fully Discrete Galerkin(DG) method for solving ini- tial value fractional integro-differential equations(FIDEs). We consider Generalized Jacobi polynomials(CJPs) with indexes corresponding to the number of homogeneous initial conditions as natural basis functions for the approximate solution. The fractional derivatives are used in the Caputo sense. The numerical solvability of algebraic system obtained from implementation of proposed method for a special case of FIDEs is investigated. We also provide a suitable convergence analysis to approximate solutions under a more general regularity assumption on the exact solution. Numerical results are presented to demonstrate the effectiveness of the proposed method. 展开更多
关键词 Fractional integro-differential equation(FIDE) Discrete Galerkin(DG) Generalized Jacobi Polynomials(GJPs) Caputo derivative
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Numerical Solution of Integro-Differential Equations with Local Polynomial Regression 被引量:1
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作者 Liyun Su Tianshun Yan +2 位作者 Yanyong Zhao Fenglan Li Ruihua Liu 《Open Journal of Statistics》 2012年第3期352-355,共4页
In this paper, we try to find numerical solution of y'(x)= p(x)y(x)+g(x)+λ∫ba K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b or y'(x)= p(x)y(x)+g(x)+λ∫xa K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b by using Local p... In this paper, we try to find numerical solution of y'(x)= p(x)y(x)+g(x)+λ∫ba K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b or y'(x)= p(x)y(x)+g(x)+λ∫xa K(x, t)y(t)dt, y(a)=α. a≤x≤b, a≤t≤b by using Local polynomial regression (LPR) method. The numerical solution shows that this method is powerful in solving integro-differential equations. The method will be tested on three model problems in order to demonstrate its usefulness and accuracy. 展开更多
关键词 integro-differential equationS Local POLYNOMIAL Regression KERNEL FUNCTIONS
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EXISTENCE AND UNIQUENESS RESULTS FOR BOUNDARY VALUE PROBLEMS OF HIGHER ORDER FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS INVOLVING GRONWALL'S INEQUALITY IN BANACH SPACES 被引量:2
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作者 Dimplekumar N. CHALISHAJAR K. KARTHIKEYAN 《Acta Mathematica Scientia》 SCIE CSCD 2013年第3期758-772,共15页
We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ (n-1, n) in Banach spaces. Existence and uniqueness results of solutions are established by vi... We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ (n-1, n) in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder's inequality, a suitable singular Cronwall's inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results. 展开更多
关键词 Boundary value problems fractional order integro-differential equations bound-ary value problems existence and uniqueness singular gronwall inequality fixed point theorem
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Numerical Algorithms for Solving One Type of Singular Integro-Differential Equation Containing Derivatives of the Time Delay States 被引量:1
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作者 Shihchung Chiang Terry L. Herdman 《Applied Mathematics》 2015年第8期1294-1301,共8页
This study presents numerical algorithms for solving a class of equations that partly consists of derivatives of the unknown state at previous certain times, as well as an integro-differential term containing a weakly... This study presents numerical algorithms for solving a class of equations that partly consists of derivatives of the unknown state at previous certain times, as well as an integro-differential term containing a weakly singular kernel. These equations are types of integro-differential equation of the second kind and were originally obtained from an aeroelasticity problem. One of the main contributions of this study is to propose numerical algorithms that do not involve transforming the original equation into the corresponding Volterra equation, but still enable the numerical solution of the original equation to be determined. The feasibility of the proposed numerical algorithm is demonstrated by applying examples in measuring the maximum errors with exact solutions at every computed nodes and calculating the corresponding numerical rates of convergence thereafter. 展开更多
关键词 integro-differential equation of the Second KIND WEAKLY SINGULAR KERNEL Numerical Algorithms Rates of Convergence
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Boundary Value Problems for Second-order Integro-differential Equations in Banach Spaces 被引量:1
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作者 莫海平 郭林 《Northeastern Mathematical Journal》 CSCD 2002年第2期183-188,共6页
This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a c... This paper investigates the maximal and minimal solutions of initial value problems for second order nonlinear integro-differential equations of Volterra type on a finite interval in a Banach space by establishing a comparison result and using the monotone iterative technique. 展开更多
关键词 integro-differential equation ordered Banacb space comparison theorem monotone iterative technique
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THE APPROXIMATION SOLUTIONS FOR HIGHER DIMENSIONAL INTEGRO-DIFFERENTIAL EQUATIONS
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作者 Lüping CHEN 《Acta Mathematica Scientia》 SCIE CSCD 2019年第5期1309-1318,共10页
This work deals with approximation solutions to a type of integro-differential equations in several complex variables. It concerns the Cauchy formula on higher dimensional domains. In our study, we make use of multipl... This work deals with approximation solutions to a type of integro-differential equations in several complex variables. It concerns the Cauchy formula on higher dimensional domains. In our study, we make use of multiple power series expansions and an iterative computation method to solve a kind of integro-differential equation. We introduce a symmetrized topology product area which is called a bicylinder. We expand functions and derivatives of them to power series. Moreover we obtain unknown functions by comparing coefficients of the series on both sides of equations. We express the approximation solutions by a regular product of matrixes. 展开更多
关键词 integro-differential equationS POLYNOMIAL approach CAUCHY FORMULA bicylinder
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REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH JUMPS AND VISCOSITY SOLUTION OF SECOND ORDER INTEGRO-DIFFERENTIAL EQUATION WITHOUT MONOTONICITY CONDITION: CASE WITH THE MEASURE OF LéVY INFINITE
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作者 Lamine SYLLA 《Acta Mathematica Scientia》 SCIE CSCD 2019年第3期819-844,共26页
We consider the problem of viscosity solution of integro-partial differential equation( IPDE in short) with one obstacle via the solution of reflected backward stochastic dif ferential equations(RBSDE in short) with j... We consider the problem of viscosity solution of integro-partial differential equation( IPDE in short) with one obstacle via the solution of reflected backward stochastic dif ferential equations(RBSDE in short) with jumps. We show the existence and uniqueness of a continuous viscosity solution of equation with non local terms, if the generator is not monotonous and Levy's measure is infinite. 展开更多
关键词 integro-partial DIFFERENTIAL equation reflected stochastic DIFFERENTIAL equations with JUMPS viscosity solution NON-LOCAL operator
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MIXED FINITE ELEMENTS FOR PARABOLICINTEGRO-DIFFERENTIAL EQUATIONS
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作者 孙澎涛 《Acta Mathematica Scientia》 SCIE CSCD 1997年第3期319-329,共11页
In this paper, we study mixed finite elements for parabolic integro-differential equations, and introduce a kind of nonclassical mixed projection, its optimal L-2 and h(-s) estimates are obtained. We define semi-discr... In this paper, we study mixed finite elements for parabolic integro-differential equations, and introduce a kind of nonclassical mixed projection, its optimal L-2 and h(-s) estimates are obtained. We define semi-discrete and full-discrete mixed finite elements for the equations, and obtain the optimal L-2 error estimates. 展开更多
关键词 integro-differential equations mixed finite element error estimates
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