Second order Jacobi approximation with applications to fourth-order differential equations

被引：20
|
作者：
Guo, BY [1 ]
Wang, ZQ
Wan, ZS
Chu, DL
机构：
[1] Shanghai Normal Univ, Dept Math, Div Comp Sci, E Inst, Shanghai 200234, Peoples R China
[2] Shanghai Univ, Dept Math, Shanghai 200436, Peoples R China
[3] Natl Univ Singapore, Dept Math, Singapore 117543, Singapore
来源：
APPLIED NUMERICAL MATHEMATICS | 2005年 / 55卷 / 04期
关键词：
second order Jacobi approximation; spectral method for fourth-order problems; convergence; numerical results;
D O I：
10.1016/j.apnum.2005.01.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Second order Jacobi approximation in non-uniformly weighted Sobolev space is investigated. Some approximation results on various orthogonal projections are established, which serve as the mathematical foundation of Jacobi spectral methods for differential equations of fourth order. Jacobi spectral schemes are provided for several model problems. The convergence is proved. Numerical results agree well with theoretical analysis and show the efficiency of this new approach. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.
引用
收藏
页码：480 / 502
页数：23
相关论文
共 50 条
  • [21] Oscillatory Properties of Fourth-Order Advanced Differential Equations
    Almutairi, Alanoud
    Ali, Ali Hasan
    Bazighifan, Omar
    Iambor, Loredana Florentina
    MATHEMATICS, 2023, 11 (06)
  • [22] On the asymptotic behavior of fourth-order functional differential equations
    Osama Moaaz
    Elmetwally M Elabbasy
    Omar Bazighifan
    Advances in Difference Equations, 2017
  • [23] Asymptotic theory for a class of fourth-order differential equations
    AlHammadi, ASA
    MATHEMATIKA, 1996, 43 (85) : 198 - 208
  • [24] Oscillation Theorems for Nonlinear Differential Equations of Fourth-Order
    Moaaz, Osama
    Dassios, Ioannis
    Bazighifan, Omar
    Muhib, Ali
    MATHEMATICS, 2020, 8 (04)
  • [25] POSITIVE SOLUTIONS OF FOURTH-ORDER ORDINARY DIFFERENTIAL EQUATIONS
    马如云
    张凤然
    ActaMathematicaScientia, 1998, (S1) : 124 - 128
  • [26] On the asymptotic behavior of fourth-order functional differential equations
    Moaaz, Osama
    Elabbasy, Elmetwally M.
    Bazighifan, Omar
    ADVANCES IN DIFFERENCE EQUATIONS, 2017,
  • [27] Asymptotic problems for fourth-order nonlinear differential equations
    Bartusek, Miroslav
    Dosla, Zuzana
    BOUNDARY VALUE PROBLEMS, 2013,
  • [28] GREEN'S FUNCTIONS FOR THE FOURTH-ORDER DIFFERENTIAL EQUATIONS
    Bouakkaz, Ahleme
    Ardjouni, Abdelouaheb
    Khemis, Rabah
    Djoudi, Ahcene
    MEMOIRS ON DIFFERENTIAL EQUATIONS AND MATHEMATICAL PHYSICS, 2019, 77 : 13 - 41
  • [29] On fourth-order nonlinear differential equations with the Painlevé property
    V. I. Gromak
    Differential Equations, 2006, 42 : 1076 - 1085
  • [30] On fourth-order nonlinear differential equations with the Painleve property
    Gromak, V. I.
    DIFFERENTIAL EQUATIONS, 2006, 42 (08) : 1076 - 1085
12345