The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves

被引：57

作者：

Dehghan, Mehdi ^{[1
]}

Fakhar-Izadi, Farhad ^{[1
]}

机构：

[1] Amirkabir Univ Technol, Fac Math & Comp Sci, Dept Appl Math, Tehran 15914, Iran

来源：

MATHEMATICAL AND COMPUTER MODELLING | 2011年 / 53卷 / 9-10期

关键词：

Modified Korteweg-de Vries (mKdV) equation; Ostrovsky equation; Collocation method; Quartic B-spline; Discrete Fourier series; Chebyshev polynomials; RADIAL BASIS FUNCTIONS; OSTROVSKY EQUATION; SOLITARY WAVES; NUMERICAL-SOLUTION; GENERALIZED KDV; MKDV EQUATION; TAU METHOD; STABILITY;

D O I：

10.1016/j.mcm.2011.01.011

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

Ostrovsky equation (modified Korteweg-de Vries equation) is used for modeling of a weakly nonlinear surface and internal waves in a rotating ocean. The Ostrovsky equation is a nonlinear partial differential equation and also is complicated due to a nonlinear integral operator as well as spatial and temporal derivatives. In this paper we propose a numerical scheme for solving this equation. Our numerical method is based on a collocation method with three different bases such as B-spline, Fourier and Chebyshev. A numerical comparison of these schemes is also provided by three examples. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1865 / 1877

页数：13

共 50 条

[11] Spectral iterative method and convergence analysis for solving nonlinear fractional differential equation
Yarmohammadi, M.
Javadi, S.
Babolian, E.
JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 359 : 436 - 450
[12] An Efficient Alternating Direction Explicit Method for Solving a Nonlinear Partial Differential Equation
Pourghanbar, Somayeh
Manafian, Jalil
Ranjbar, Mojtaba
Aliyeva, Aynura
Gasimov, Yusif S.
MATHEMATICAL PROBLEMS IN ENGINEERING, 2020, 2020 (2020)
[13] Sinc–Muntz–Legendre Collocation Method for Solving a Class of Nonlinear Fractional Partial Differential Equations
M. Shareef Ajeel
M. Gachpazan
Ali R. Soheili
Computational Mathematics and Mathematical Physics, 2021, 61 : 2024 - 2033
[14] Pell Collocation Method for Solving the Nonlinear Time-Fractional Partial Integro-Differential Equation with a Weakly Singular Kernel
Taghipour, M.
Aminikhah, H.
JOURNAL OF FUNCTION SPACES, 2022, 2022
[15] Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation
Singh, Swarn
Bhatt, Sandeep
Singh, Suruchi
COMPUTATIONAL METHODS FOR DIFFERENTIAL EQUATIONS, 2022, 10 (01): : 28 - 43
[16] A spectral collocation method for a nonlinear multidimensional Volterra integral equation
Zheng, Weishan
Chen, Yanping
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2023, 39 (02) : 1767 - 1777
[17] The spectral collocation method for solving a fractional integro-differential equation
Wu, Chuanhua
Wang, Ziqiang
AIMS MATHEMATICS, 2022, 7 (06): : 9577 - 9587
[18] Convergence rate of collocation method based on wavelet for nonlinear weakly singular partial integro-differential equation arising from viscoelasticity
Singh, Somveer
Patel, Vijay Kumar
Singh, Vineet Kumar
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2018, 34 (05) : 1781 - 1798
[19] LEGENDRE SPECTRAL COLLOCATION METHOD FOR SECOND-ORDER NONLINEAR ORDINARY/PARTIAL DIFFERENTIAL EQUATIONS
Yi, Lijun
Wang, Zhongqing
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2014, 19 (01): : 299 - 322
[20] Spectral collocation method for nonlinear Caputo fractional differential system
Gu, Zhendong
ADVANCES IN COMPUTATIONAL MATHEMATICS, 2020, 46 (05)

← 1 2 3 4 5 →