Two-dimensional Legendre wavelets for solving fractional Poisson equation with Dirichlet boundary conditions

被引：73
|
作者：
Heydari, M. H. [1 ]
Hooshmandasl, M. R. [1 ]
Ghaini, F. M. Maalek [1 ]
Fereidouni, F. [2 ]
机构：
[1] Yazd Univ, Fac Math, Yazd, Iran
[2] Yazd Univ, Fac Min Engn, Yazd, Iran
来源：
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS | 2013年 / 37卷 / 11期
关键词：
Legendre wavelets; Poisson equation; Dirichlet boundary condition; Fractional derivative; NUMERICAL-SOLUTION;
D O I：
10.1016/j.enganabound.2013.07.002
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
In this paper, the two-dimensional Legendre wavelets are applied for numerical solution of the fractional Poisson equation with Dirichlet boundary conditions. In this way, a new operational matrix of fractional derivative for the Legendre wavelets is derived and then this operational matrix has been employed to obtain the numerical solution of the above-mentioned problem. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifies the problem. The convergence of the two-dimensional Legendre wavelets expansion is investigated. Also the power of this manageable method is illustrated. (C) 2013 Elsevier Ltd. All rights reserved.
引用
收藏
页码：1331 / 1338
页数：8
相关论文
共 50 条
  • [11] ON THE DERIVATION OF HIGHEST-ORDER COMPACT FINITE DIFFERENCE SCHEMES FOR THE ONE- AND TWO-DIMENSIONAL POISSON EQUATION WITH DIRICHLET BOUNDARY CONDITIONS
    Settle, Sean O.
    Douglas, Craig C.
    Kim, Imbunm
    Sheen, Dongwoo
    SIAM JOURNAL ON NUMERICAL ANALYSIS, 2013, 51 (04) : 2470 - 2490
  • [12] Block pulse functions for solving fractional Poisson type equations with Dirichlet and Neumann boundary conditions
    Jiaquan Xie
    Qingxue Huang
    Fuqiang Zhao
    Hailian Gui
    Boundary Value Problems, 2017
  • [13] Block pulse functions for solving fractional Poisson type equations with Dirichlet and Neumann boundary conditions
    Xie, Jiaquan
    Huang, Qingxue
    Zhao, Fuqiang
    Gui, Hailian
    BOUNDARY VALUE PROBLEMS, 2017,
  • [14] Numerical analysis of variable fractional viscoelastic column based on two-dimensional Legendre wavelets algorithm
    Sun, Lin
    Chen, Yiming
    CHAOS SOLITONS & FRACTALS, 2021, 152
  • [15] Solving a Two-Dimensional Nonlinear Heat Conduction Equation with Nonzero Boundary Conditions by the Boundary Element Method
    Spevak, L. F.
    Nefedova, O. A.
    MECHANICS, RESOURCE AND DIAGNOSTICS OF MATERIALS AND STRUCTURES (MRDMS-2017), 2017, 1915
  • [16] Application of Bernoulli matrix method for solving two-dimensional hyperbolic telegraph equations with Dirichlet boundary conditions
    Singh, Somveer
    Patel, Vijay Kumar
    Singh, Vineet Kumar
    Tohidi, Emran
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 75 (07) : 2280 - 2294
  • [17] Two-dimensional shifted Legendre polynomials operational matrix method for solving the two-dimensional integral equations of fractional order
    Hesameddini, Esmail
    Shahbazi, Mehdi
    APPLIED MATHEMATICS AND COMPUTATION, 2018, 322 : 40 - 54
  • [18] ON LEGENDRE WAVELETS FOR POISSON EQUATION IN THE FRAME OF COMPLEX SOLUTION
    Kerrouche, Nacereddine
    Kadem, Abdelouahab
    PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS, 2022, 48 : 153 - 167
  • [19] The two-dimensional heat equation with nonlocal boundary conditions
    N. I. Ionkin
    V. A. Morozova
    Differential Equations, 2000, 36 : 982 - 987
  • [20] The two-dimensional heat equation with nonlocal boundary conditions
    Ionkin, NI
    Morozova, VA
    DIFFERENTIAL EQUATIONS, 2000, 36 (07) : 982 - 987
12345