Meshless Method of Lines for Numerical Solution of Kawahara Type Equations - Applied Mathematics

AM > Vol.2 No.5, May 2011

Applied Mathematics

Volume 2, Issue 5 (May 2011)

ISSN Print: 2152-7385 ISSN Online: 2152-7393

Google-based Impact Factor: 0.96 Citations

Meshless Method of Lines for Numerical Solution of Kawahara Type Equations ()

HTML

Download as PDF (Size: 436KB) PP. 608-618

DOI: 10.4236/am.2011.25081 6,520 Downloads 12,909 Views Citations

Author(s)

Nagina Bibi, Syed Ikram Abbas Tirmizi, Sirajul Haq

Affiliation(s)

ABSTRACT

In this work, an algorithm based on method of lines coupled with radial basis functions namely meshless method of lines (MMOL) is presented for the numerical solution of Kawahara, modified Kawahara and KdV Kawahara equations. The motion of a single solitary wave, interaction of two and three solitons and the phenomena of wave generation is discussed. The results are compared with the exact solution and with the results in the relevant literature to show the efficiency of the method.

KEYWORDS

Kawahara Type Equations, Meshless Method of Lines (MMOL), Radial Basis Functions (Rbfs)

Share and Cite:

Bibi, N. , Tirmizi, S. and Haq, S. (2011) Meshless Method of Lines for Numerical Solution of Kawahara Type Equations. Applied Mathematics, 2, 608-618. doi: 10.4236/am.2011.25081.

Cited by

[1]	A Bernstein Polynomial Differential Quadrature Method for Numerical Solutions of Kawahara Equation
	International Journal of Convergence in Healthcare, 2024

[2]	A composite method based on delta‐shaped basis functions and Lie group high‐order geometric integrator for solving Kawahara‐type equations
	Mathematical Methods in the Applied …, 2023

[3]	Nonic B-spline algorithms for numerical solution of the Kawahara equation
	Turkish Journal of Mathematics, 2022

[4]	A meshless two-stage scheme for the fifth-order dispersive models in the science of waves on water
	Ocean Engineering, 2022

[5]	Modifiye edilmiş Kawahara ve genelleştirilmiş Rosenau Kawahara RLW denklemleri için kollokasyon yöntemi
	2022

[6]	On the dissipative extended Kawahara solitons and cnoidal waves in a collisional plasma: Novel analytical and numerical solutions
	Tantawy, AH Salas, MR Alharthi - Physics of Fluids, 2021

[7]	Conservative compact difference scheme based on the scalar auxiliary variable method for the generalized Kawahara equation
	Mathematical Methods in the Applied Sciences, 2021

[8]	Solution of Kawahara equation using a predictor-corrector and RBF-QR method
	2021

[9]	Bell-shaped soliton solutions and travelling wave solutions of the fifth-order nonlinear modified Kawahara equation
	2020

[10]	Numerical solution for the Kawahara equation using local RBF-FD meshless method
	2020

[11]	Performance of compact and non-compact structure preserving algorithms to traveling wave solutions modeled by the Kawahara equation
	2020

[12]	Highly efficient approach to numerical solutions of two different forms of the modified Kawahara equation via contribution of two effective methods
	2020

[13]	An Efficient Approximation to Numerical Solutions for the Kawahara Equation Via Modified Cubic B-Spline Differential Quadrature Method
	2019

[14]	Numerical solution of time-fractional Kawahara equation using reproducing kernel method with error estimate
	2019

[15]	Generalized Fractional Order Differential Equations Arising in Physical Models
	2018

[16]	Kesir mertebeli türev içeren bazı kısmi türevli diferansiyel denklemlerin doğuran çekirdekli hilbert uzayı metodu ile nümerik çözümlerinin incelenmesi
	2018

[17]	Bazı sığ su dalga denklemlerinin sonlu elemanlar yöntemi ile sayısal çözümleri
	2017

[18]	New exact solutions of time fractional modified Kawahara equations in modelling surface tension in shallow-water and capillary gravity water waves
	The European Physical Journal Plus, 2017

[19]	Numerical Solution of Advection–Diffusion Equation Using Meshless Method of Lines
	Iranian Journal of Science and Technology, Transactions A: Science, 2017

[20]	A novel analytical solution for the modified Kawahara equation using the residual power series method
	Nonlinear Dynamics, 2017

[21]	Two New Energy-Preserving Algorithms for Generalized Fifth-Order KdV Equation
	Advances in Applied Mathematics and Mechanics, 2017

[22]	B-SPLINE COLLOCATION METHOD FOR NUMERICAL SOLUTION OF NONLINEAR KAWAHARA AND MODIFIED KAWAHARA EQUATIONS
	TWMS Journal of Applied and Engineering Mathematics, 2017

[23]	A new explicit multisymplectic integrator for the Kawahara-type equation
	中国物理B: 英文版, 2014

[24]	Numerical Solution of Kawahara Equations by Using Laplace Homotope Perturbations Method
	Applied Mathematical Sciences, 2014

[25]	Numerical Solutions of Two-Way Propagation of Nonlinear Dispersive Waves Using Radial Basis Functions
	International Journal of Partial Differential Equations, 2014

[26]	Numerical solutions of the Kawahara equation by the septic B spline collocation method
	2014

[27]	Numerical solutions of the Kawahara equation by the septic B-spline collocation method
	2014

[28]	Adaptive radial basis function interpolation for time-dependent partial differential equations
	2013

[29]	Bazı özel evolution denklemlerinin nümerik çözümlerinin karşılaştırılması


[30]	Zaman bağımlı kısmi türevli diferensiyel denklemlerin nümerik çözümü için Lagrange interpolasyon polinomları yardımıyla ağsız çizgiler yöntemi

Journals Menu

Follow SCIRP

	customer@scirp.org
	+86 18163351462(WhatsApp)
	1655362766

	Paper Publishing WeChat

Journals Menu

Home

About SCIRP

Service

Policies