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Three-Variable Shifted jacobi Polynomials Approach for Numerically Solving Three-Dimensional Multi-Term Fractional-Order PDEs with Variable Coefficients

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Computer Modeling in Engineering & Sciences 2018年第4期115卷 67-84页

作者： Jiaquan Xie Fuqiang Zhao Zhibin Yao Jun Zhang College of Mechanical Engineering Taiyuan University of Science and TechnologyTaiyuan 030024China Taiyuan Institute of China Coal Technology Engineering Group Taiyuan 030006China Collaborative Innovation Center of Taiyuan Heavy Machinery Equipment Taiyuan 030024China.

In this paper,the three-variable shifted jacobi operational matrix of fractional derivatives is used together with the collocation method for numerical solution of threedimensional multi-term fractional-order PDEs with variable *** main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the *** approximate solutions of nonlinear fractional PDEs with variable coefficients thus obtained by threevariable shifted jacobi polynomials are compared with the exact *** some theorems and lemmas are introduced to verify the convergence results of our ***,several numerical examples are presented to test the superiority and efficiency of the proposed method.

关键词： Three-variable shifted jacobi polynomials multi-term fractional-order PDEs variable coefficients numerical solution convergence analysis

jacobi-Sobolev Orthogonal Polynomialsand Spectral Methods for Elliptic Boundary Value Problems

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Communications on Applied Mathematics and Computation 2019年第2期1卷 283-308页

作者： Xuhong Yu Zhongqing Wang Huiyuan Li University of Shanghai for Science and Technology Shanghai 200093China State Key Laboratory of Computer Science/Laboratory of Parallel Computing Institute of SoftwareChinese Academy of SciencesBeijing 100190China

Generalized jacobi polynomials with indexes α,β∈ R are introduced and some basic properties are established. As examples of applications,the second- and fourth-order elliptic boundary value problems with Dirichlet or Robin boundary conditions are considered,and the generalized jacobi spectral schemes are proposed. For the diagonalization of discrete systems,the jacobi-Sobolev orthogonal basis functions are constructed,which allow the exact solutions and the approximate solutions to be represented in the forms of infinite and truncated jacobi series. Error estimates are obtained and numerical results are provided to illustrate the effectiveness and the spectral accuracy.

关键词： Generalized jacobi polynomials Spectral method - jacobi-Sobolev orthogonal basis functions Elliptic boundary value problems Error analysis

A jacobi Spectral Collocation Scheme Based on Operational Matrix for Time-fractional Modified Korteweg-de Vries Equations

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Computer Modeling in Engineering & Sciences 2015年第3期104卷 185-209页

作者： A.H.Bhrawy E.H.Doha S.S.Ezz-Eldien M.A.Abdelkawy Department of Mathematics Faculty of ScienceKing Abdulaziz UniversityJeddahSaudi Arabia Department of Mathematics Faculty of ScienceBeni-Suef UniversityBeni-SuefEgypt Department of Mathematics Faculty of ScienceCairo UniversityGizaEgypt Department of Mathematics Faculty of ScienceAssiut UniversityNew Valley BranchEl-Kharja 72511Egypt

In this paper,a high accurate numerical approach is investigated for solving the time-fractional linear and nonlinear Korteweg-de Vries(KdV)*** equations are the most appropriate and desirable definition for physical *** spectral collocation method and the operational matrix of fractional derivatives are used together with the help of the Gauss-quadrature formula in order to reduce such problem into a problem consists of solving a system of algebraic equations which greatly simplifying the *** approach is based on the shifted jacobi polynomials and the fractional derivative is described in the sense of *** addition,the presented approach is applied also to solve the timefractional modified KdV *** testing the accuracy,validity and applicability of the developed numerical approach,we apply it to provide high accurate approximate solutions for four test problems.

关键词： KdV equation jacobi polynomials Operational matrix Gauss quadrature Collocation spectral method Caputo derivative

Some new results about jacobi forms

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Chinese Science Bulletin 1997年第3期42卷 181-183页

作者： WANG JupingDepartment of Mathematics, University of Science and Technology of China, Hefei 230026, China Department of Mathematics University of Science and Technology of China Hefei China

THE one-dimensional jacobi forms were first systematically investigated by Eichler and Zagier, and a similar theory in a higher-dimensional case was developed by Ziegler, who gave the precise definition and some basic properties of higher-dimensional jacobi forms. This note tries to give a satisfactory classification for a large kind of spaces of jacobi forms. To be a little more explicit, we get a rank formula for jacobi forms and then show that either all the

关键词： jacobi forms rank coefficient estimation.

A note on jacobi-Eisenstein series

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Chinese Science Bulletin 1998年第14期43卷 1163-1165页

作者： WANG Juping Institute of Mathematics, Fudan University, Shanghai 200433, China Institute of Mathematics Fudan University Shanghai China

The so_called jacobi_Eisenstein series is defined by E k, S (z, w)=∑y∈J ∞\J (1, j) Z 1|k, Sy(z, w) . The Fourier coefficients of E k, S is determined completely. The theorem extends the results of Eichler and Zagie... 详细信息

关键词： jacobi Eisenstein series jacobi form Fourier coefficient

A jacobi-Eisenstein series of weight two on congruence jacobi subgroup

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Science China Mathematics 2010年第9期53卷 2405-2410页

作者： LU HongWen & ZHOU HaiGang Department of Mathematics,Tongji University,Shanghai 200092,China Department of Mathematics Tongji University Shanghai China

The specific aims of this paper are to define a jacobi-Eisenstein series of weight two on congruence jacobi subgroup and to compute its Fourier expansion coefficients in *** overcome the difficulties that the jacobi-E... 详细信息

关键词： jacobi forms Eisenstein series Fourier expansion

Complex-weighted Plancherel formula and jacobi transform

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Chinese Science Bulletin 1996年第6期41卷 454-458页

作者：刘建明郑维行 Department of Mathematics Nanjing University Nanjing 210093 China

Let v∈C. We consider the complex measure dμv（z） =（1-│z│2）v-2dxdy（z=x+iy） on theunit disk D of the complex plane. Let （D） be the spaces of C∞-function on D with compactsupports and #（B） the space of radi... 详细信息

关键词： complex-weighted Plancherel formula Mobius group jacobi transform.

Theta Series and Trace Formula for jacobi Forms

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Chinese Science Bulletin 1993年第14期38卷 1150-1153页

作者：李云峰 Department of Mathematics University of Science and Technology of China Hefei 230026 PRC

1 Introduction jacobi forms are the generalization of jacobi theta series and the coefficients of the Fourier-jacobi expansion of a Siegel modular form. The theory develops systematically in recent years and has many ... 详细信息

关键词： jacobi form theta series Siegel modular form trace formula.

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jacobi椭圆函数展开解的可视化

物理学报 2005年第7期54卷 2996-2999页

作者：郑强岳萍龚伦训贵州师范大学理学院贵阳550001

作出了jacobi椭圆正弦函数sn(x,k)的图像,通过图像展示了它的一些性质;并作出了KdV方程jacobi椭圆函数展开解在两种参数下的图像.

关键词： jacobi 函数展开椭圆可视化 KdV方程正弦函数图像