On the Numerical Solution of 1D and 2D KdV Equations Using Variational Homotopy Perturbation and Finite Difference Methods
Author
Abstract
Suggested Citation
Download full text from publisher
References listed on IDEAS
- Mesfin Mekuria Woldaregay & Gemechis File Duressa, 2021. "Uniformly Convergent Hybrid Numerical Method for Singularly Perturbed Delay Convection-Diffusion Problems," International Journal of Differential Equations, Hindawi, vol. 2021, pages 1-20, September.
- Samuel, F.M. & Motsa, S.S., 2019. "A highly accurate trivariate spectral collocation method of solution for two-dimensional nonlinear initial-boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 221-235.
- Fasika Wondimu Gelu & Gemechis File Duressa, 2021. "A Uniformly Convergent Collocation Method for Singularly Perturbed Delay Parabolic Reaction-Diffusion Problem," Abstract and Applied Analysis, Hindawi, vol. 2021, pages 1-11, March.
- Syed Tauseef Mohyud-Din & Ahmet Yildirim & Sefa Anıl Sezer & Muhammad Usman, 2010. "Modified Variational Iteration Method for Free-Convective Boundary-Layer Equation Using Padé Approximation," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-11, April.
- He, Ji-Huan & Wu, Xu-Hong, 2006. "Construction of solitary solution and compacton-like solution by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 108-113.
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Assas, Laila M.B., 2008. "Variational iteration method for solving coupled-KdV equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1225-1228.
- He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
- Javidi, M. & Golbabai, A., 2008. "Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 309-313.
- Xu, Lan, 2009. "The variational iteration method for fourth order boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1386-1394.
- Kuru, S., 2009. "Compactons and kink-like solutions of BBM-like equations by means of factorization," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 626-633.
- Xu, Lan, 2008. "Variational approach to solitons of nonlinear dispersive K(m,n) equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 137-143.
- Moghimi, Mahdi & Hejazi, Fatemeh S.A., 2007. "Variational iteration method for solving generalized Burger–Fisher and Burger equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1756-1761.
- Wang, Shu-Qiang & He, Ji-Huan, 2008. "Nonlinear oscillator with discontinuity by parameter-expansion method," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 688-691.
- Borhanifar, A. & Kabir, M.M. & Maryam Vahdat, L., 2009. "New periodic and soliton wave solutions for the generalized Zakharov system and (2+1)-dimensional Nizhnik–Novikov–Veselov system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1646-1654.
- He, Ji-Huan, 2007. "Variational approach for nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1430-1439.
- Darvishi, M.T. & Khani, F., 2009. "Numerical and explicit solutions of the fifth-order Korteweg-de Vries equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2484-2490.
- Jules Sadefo-Kamdem, 2011. "Integral Transforms With The Homotopy Perturbation Method And Some Applications," Working Papers hal-00580023, HAL.
- (Benn)Wu, Xu-Hong & He, Ji-Huan, 2008. "EXP-function method and its application to nonlinear equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 903-910.
- Odibat, Zaid M., 2009. "Exact solitary solutions for variants of the KdV equations with fractional time derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1264-1270.
- Syam, Muhammed I. & Siyyam, Hani I., 2009. "An efficient technique for finding the eigenvalues of fourth-order Sturm–Liouville problems," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 659-665.
- Soliman, A.A., 2009. "On the solution of two-dimensional coupled Burgers’ equations by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1146-1155.
- Da-Quan, Xian & Zheng-De, Dai, 2009. "Application of Exp-function method to potential Kadomtsev–Petviashvili equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2653-2659.
- Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
- Ali, A.H.A. & Raslan, K.R., 2009. "Variational iteration method for solving partial differential equations with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1520-1529.
- Yin, Jiuli & Tian, Lixin, 2009. "Stumpons and fractal-like wave solutions to the Dullin–Gottwald–Holm equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 643-648.
More about this item
Keywords
linear and non-linear KdV equations; homogeneous; non-homogeneous; variational homotopy perturbation method; classical finite difference method; stability; consistency;All these keywords.
Statistics
Access and download statisticsCorrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4443-:d:983450. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.