Relevant bibliographies by topics / Petviashvili iteration

Academic literature on the topic 'Petviashvili iteration'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Contents

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Petviashvili iteration.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Petviashvili iteration"

1

Zhao, Dexu, Raghda A. M. Attia, Jian Tian, Samir A. Salama, Dianchen Lu, and Mostafa M. A. Khater. "Abundant accurate analytical and semi-analytical solutions of the positive Gardner–Kadomtsev–Petviashvili equation." Open Physics 20, no. 1 (January 1, 2022): 30–39. http://dx.doi.org/10.1515/phys-2022-0001.

Full text
Abstract:
Abstract This research article examines the correctness of two new analytical methods for solving the internal solitary waves of shallow seas. To get the computational solutions to the positive (2 + 1)-dimensional Gardner–Kadomtsev–Petviashvili model, the extended simplest equation and modified Kudryashov methods are used. Numerous new traveling wave solutions in various forms are developed in order to assess the starting conditions required for the variational iteration technique, one of the most accurate semi-analytical methods. The semi-analytical solutions are used to demonstrate the precision of the solutions obtained and the analytical methods employed. The dynamical behavior of internal solitary waves in shallow waters is shown using many three-dimensional drawings. The performance of the used schemes demonstrates their efficacy and power, as well as their capacity to handle a large number of nonlinear evolution equations.
APA, Harvard, Vancouver, ISO, and other styles
2

Lakoba, T. I., and J. Yang. "A generalized Petviashvili iteration method for scalar and vector Hamiltonian equations with arbitrary form of nonlinearity." Journal of Computational Physics 226, no. 2 (October 2007): 1668–92. http://dx.doi.org/10.1016/j.jcp.2007.06.009.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Li, Wu, Lanre Akinyemi, Dianchen Lu, and Mostafa M. A. Khater. "Abundant Traveling Wave and Numerical Solutions of Weakly Dispersive Long Waves Model." Symmetry 13, no. 6 (June 17, 2021): 1085. http://dx.doi.org/10.3390/sym13061085.

Full text
Abstract:
In this article, plenty of wave solutions of the (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony ((2 + 1)-D KP-BBM) model are constructed by employing two recent analytical schemes (a modified direct algebraic (MDA) method and modified Kudryashov (MK) method). From the point of view of group theory, the proposed analytical methods in our article are based on symmetry, and effectively solve those problems which actually possess explicit or implicit symmetry. This model is a vital model in shallow water phenomena where it demonstrates the wave surface propagating in both directions. The obtained analytical solutions are explained by plotting them through 3D, 2D, and contour sketches. These solutions’ accuracy is also tested by calculating the absolute error between them and evaluated numerical results by the Adomian decomposition (AD) method and variational iteration (VI) method. The considered numerical schemes were applied based on constructed initial and boundary conditions through the obtained analytical solutions via the MDA, and MK methods which show the synchronization between computational and numerical obtained solutions. This coincidence between the obtained solutions is explained through two-dimensional and distribution plots. The applied methods’ symmetry is shown through comparing their obtained results and showing the matching between both obtained solutions (analytical and numerical).
APA, Harvard, Vancouver, ISO, and other styles
4

Hızela, Emanullah, and Semih Küçükarslan. "Homotopy Perturbation Method for Higher Dimensional Nonlinear Evolutionary Equations." Zeitschrift für Naturforschung A 64, no. 9-10 (October 1, 2009): 568–74. http://dx.doi.org/10.1515/zna-2009-9-1005.

Full text
Abstract:
In this paper, an iterative numerical solution of the higher-dimensional (3+1) physically important nonlinear evolutionary equations is studied by using the homotopy perturbation method (HPM). For this purpose, the Kadomstev-Petviashvili (KP) and the Jumbo-Miwa (JM) equations are analyzed with the HPM and the available exact solutions obtained by the homogenous balance method will be compared to show the accuracy of the proposed numerical algorithm. The results approves the effectiveness and accuracy of the HPM.
APA, Harvard, Vancouver, ISO, and other styles
5

Clamond, Didier, and Denys Dutykh. "Accurate fast computation of steady two-dimensional surface gravity waves in arbitrary depth." Journal of Fluid Mechanics 844 (April 6, 2018): 491–518. http://dx.doi.org/10.1017/jfm.2018.208.

Full text
Abstract:
This paper describes an efficient algorithm for computing steady two-dimensional surface gravity waves in irrotational motion. The algorithm complexity is $O(N\log N)$, $N$ being the number of Fourier modes. This feature allows the arbitrary precision computation of waves in arbitrary depth, i.e. it works efficiently for Stokes, cnoidal and solitary waves, even for quite large steepnesses, up to approximately 99 % of the maximum steepness for all wavelengths. In particular, the possibility to compute very long (cnoidal) waves accurately is a feature not shared by other algorithms and asymptotic expansions. The method is based on conformal mapping, the Babenko equation rewritten in a suitable way, the pseudo-spectral method and Petviashvili iterations. The efficiency of the algorithm is illustrated via some relevant numerical examples. The code is open source, so interested readers can easily check the claims, use and modify the algorithm.
APA, Harvard, Vancouver, ISO, and other styles
6

Pelinovsky, Dmitry E., and Yury A. Stepanyants. "Convergence of Petviashvili's Iteration Method for Numerical Approximation of Stationary Solutions of Nonlinear Wave Equations." SIAM Journal on Numerical Analysis 42, no. 3 (January 2004): 1110–27. http://dx.doi.org/10.1137/s0036142902414232.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Frasca-Caccia, Gianluca, and Peter E. Hydon. "A New Technique for Preserving Conservation Laws." Foundations of Computational Mathematics, May 19, 2021. http://dx.doi.org/10.1007/s10208-021-09511-1.

Full text
Abstract:
AbstractThis paper introduces a new symbolic-numeric strategy for finding semidiscretizations of a given PDE that preserve multiple local conservation laws. We prove that for one spatial dimension, various one-step time integrators from the literature preserve fully discrete local conservation laws whose densities are either quadratic or a Hamiltonian. The approach generalizes to time integrators with more steps and conservation laws of other kinds; higher-dimensional PDEs can be treated by iterating the new strategy. We use the Boussinesq equation as a benchmark and introduce new families of schemes of order two and four that preserve three conservation laws. We show that the new technique is practicable for PDEs with three dependent variables, introducing as an example new families of second-order schemes for the potential Kadomtsev–Petviashvili equation.
APA, Harvard, Vancouver, ISO, and other styles
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography