Numerical investigation of multiple periodic solutions of fourth-order semi-linear ODE

被引：0
|
作者：
Chaparova, Julia V. [1 ]
Kalcheva, Eli P. [1 ]
Koleva, Miglena N. [1 ]
机构：
[1] Univ Rousse, FNSE, Rousse 7017, Bulgaria
来源：
APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE '12) | 2012年 / 1497卷
关键词：
Fourth-order ODE; variational methods; multiple solutions; inexact-Newton method; Homotopy method; Picard method; multi-grid algorithm; convergence;
D O I：
10.1063/1.4766780
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work we consider stationary periodic solutions of fourth-order semi-linear parabolic equation, arising in population dynamics and spatial patterns formation. First, using variational method, we establish existence of infinitely many solutions. Next we develop a fast numerical algorithm for solving the model problem. Numerical results are proposed and discussed.
引用
收藏
页码：152 / 159
页数：8
相关论文
共 50 条
  • [1] Multiple solutions for a fourth-order nonlinear elliptic problem which is superlinear at +∞ and linear at −∞
    Ruichang Pei
    Jihui Zhang
    Boundary Value Problems, 2014
  • [2] Existence of periodic solutions of fourth-order nonlinear difference equations
    Shi, Haiping
    Liu, Xia
    Zhang, Yuanbiao
    Deng, Xiaoqing
    REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, 2014, 108 (02) : 811 - 825
  • [3] Multiple solutions for a fourth-order nonlinear elliptic problem
    Ruichang Pei
    Boundary Value Problems, 2012
  • [4] Multiple solutions for fourth-order boundary value problem
    Pang, CC
    Dong, W
    Wei, ZL
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 314 (02) : 464 - 476
  • [5] Multiple solutions for a fourth-order nonlinear elliptic problem
    Pei, Ruichang
    BOUNDARY VALUE PROBLEMS, 2012,
  • [6] Multiple solutions for a fourth-order nonlinear elliptic problem which is superlinear at plus ∞ and linear at -∞
    Pei, Ruichang
    Zhang, Jihui
    BOUNDARY VALUE PROBLEMS, 2014,
  • [7] Multiple solutions to fourth-order boundary value problems
    Cui, Yaqiong
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 57 (04) : 643 - 649
  • [8] Multiple solutions for a perturbed fourth-order Kirchhoff type elliptic problem
    Heidarkhani, Shapour
    Khademloo, Somaye
    Solimaninia, Arezoo
    PORTUGALIAE MATHEMATICA, 2014, 71 (01) : 39 - 61
  • [9] Hessian discretisation method for fourth-order semi-linear elliptic equations: applications to the von Karman and Navier-Stokes models
    Droniou, Jerome
    Nataraj, Neela
    Shylaja, Devika
    ADVANCES IN COMPUTATIONAL MATHEMATICS, 2021, 47 (02)
  • [10] Multiple solutions for the fourth-order elliptic equation with vanishing potential
    Zhang, Wen
    Zhang, Jian
    Luo, Zhiming
    APPLIED MATHEMATICS LETTERS, 2017, 73 : 98 - 105
12345