A Meshless Method of Lines for Numerical Solution of Some Coupled Nonlinear Evolution Equations

2014 ◽  
Vol 15 (2) ◽  
Author(s):  
Arshed Ali ◽  
Fazal Haq ◽  
Iltaf Hussain ◽  
Usman Shah
Keyword(s):  
Numerical Solution ◽  
Meshless Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Method Of Lines ◽  
Nonlinear Evolution Equations ◽  
Meshless Method Of Lines

scholarly journals Exact and Numerical Solitary Wave Structures to the Variant Boussinesq System

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1473 ◽  
Author(s):  
Abdulghani Alharbi ◽  
Mohammed B. Almatrafi
Keyword(s):  
Solitary Wave ◽  
Evolution Equations ◽  
Numerical Solutions ◽  
Nonlinear Evolution ◽  
Numerical Technique ◽  
Method Of Lines ◽  
Nonlinear Evolution Equations ◽  
Boussinesq System ◽  
Solitary Wave Solutions ◽  
The Method Of Lines

Solutions such as symmetric, periodic, and solitary wave solutions play a significant role in the field of partial differential equations (PDEs), and they can be utilized to explain several phenomena in physics and engineering. Therefore, constructing such solutions is significantly essential. This article concentrates on employing the improved exp(−ϕ(η))-expansion approach and the method of lines on the variant Boussinesq system to establish its exact and numerical solutions. Novel solutions based on the solitary wave structures are obtained. We present a comprehensible comparison between the accomplished exact and numerical results to testify the accuracy of the used numerical technique. Some 3D and 2D diagrams are sketched for some solutions. We also investigate the L2 error and the CPU time of the used numerical method. The used mathematical tools can be comfortably invoked to handle more nonlinear evolution equations.

scholarly journals Meshless Method of Lines for Numerical Solution of Kawahara Type Equations

2011 ◽  
Vol 02 (05) ◽  
pp. 608-618 ◽  
Author(s):  
Nagina Bibi ◽  
Syed Ikram Abbas Tirmizi ◽  
Sirajul Haq
Keyword(s):  
Numerical Solution ◽  
Meshless Method ◽  
Method Of Lines ◽  
Meshless Method Of Lines

scholarly journals Numerical Solution of Heat Equation in Polar Cylindrical Coordinates by the Meshless Method of Lines

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Arshad Hussain ◽  
Marjan Uddin ◽  
Sirajul Haq ◽  
Hameed Ullah Jan
Keyword(s):  
Heat Equation ◽  
Numerical Solution ◽  
Meshless Method ◽  
Method Of Lines ◽  
Time Integration ◽  
Cylindrical Coordinates ◽  
Runge Kutta Method ◽  
Radial Basis ◽  
Rectangular Coordinates ◽  
Meshless Method Of Lines

We propose a numerical solution to the heat equation in polar cylindrical coordinates by using the meshless method of lines approach. The space variables are discretized by multiquadric radial basis function, and time integration is performed by using the Runge-Kutta method of order 4. In radial basis functions (RBFs), much of the research are devoted to the partial differential equations in rectangular coordinates. This work is an attempt to explore the versatility of RBFs in nonrectangular coordinates as well. The results show that application of RBFs is equally good in polar cylindrical coordinates. Comparison with other cited works confirms that the present approach is accurate as well as easy to implement to problems in higher dimensions.

A wavelet-based method for numerical solution of nonlinear evolution equations

2000 ◽  
Vol 33 (1-4) ◽  
pp. 291-297 ◽  
Author(s):  
Valeriano Comincioli ◽  
Giovanni Naldi ◽  
Terenzio Scapolla
Keyword(s):  
Numerical Solution ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations

Construction of the numerical and analytical wave solutions of the Joseph–Egri dynamical equation for the long waves in nonlinear dispersive systems

2020 ◽  
Vol 34 (30) ◽  
pp. 2050289
Author(s):  
Abdulghani R. Alharbi ◽  
M. B. Almatrafi ◽  
Aly R. Seadawy
Keyword(s):  
Solitary Wave ◽  
Numerical Solution ◽  
Evolution Equations ◽  
Dynamical Equation ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Nonlinear Evolution Equations ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
The Stability

The Kudryashov technique is employed to extract several classes of solitary wave solutions for the Joseph–Egri equation. The stability of the achieved solutions is tested. The numerical solution of this equation is also investigated. We also present the accuracy and the stability of the numerical schemes. Some two- and three-dimensional figures are shown to present the solutions on some specific domains. The used methods are found useful to be applied on other nonlinear evolution equations.

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