Numerical Solutions of Two-Way Propagation of Nonlinear Dispersive Waves Using Radial Basis Functions

Suarez, Pablo; Morales, J. Héctor

doi:10.1155/2014/407387

Cited by 3 publications

(2 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this example, we will take 𝑐 0 = 𝑐 1 = 1, and the different values of 𝛽 and 𝑘, as we shall in the tables, also we chose Multiquadric radial base function with 𝜀 = 5. The accuracy of the methods is tested by computing the absolute error 𝐿 𝑎𝑏𝑠 , which is defined as in (Suarez and Morales, 2014;Yao et al, 2012) by the following formula:…”

Section: Numerical Examplesmentioning

confidence: 99%

Numerical Solution of Hirota-satsuma Coupled Kdv System by Rbf-ps Method

Sadeeq

Omar²,

Pirdawood³

2022

UOD

View full text Add to dashboard Cite

In this paper, the Hirota-Satsuma coupled Korteweg-de Vries system is solved numerically by using radialbasis function-Pseudospectral method. The radial basis functions are used to approximate the space derivatives in the system. Moreover, the system has become a system of ordinary differential equations with independent variable , and this system is solved by Runge-Kutta fourth order method, with the help of MATLAB R2020a. Also, a comparison has been made between approximate solutions obtained by the proposed method and exact solutions

show abstract

Section: Numerical Examplesmentioning

confidence: 99%

Numerical Solution of Hirota-satsuma Coupled Kdv System by Rbf-ps Method

Sadeeq

Omar²,

Pirdawood³

2022

UOD

View full text Add to dashboard Cite

show abstract

“…The problems with homogenous Dirichlet, reflection, and periodic boundary conditions were integrated by Galerkin-finite element combined with fourth order explicit Runge-Kutta method. A meshless radial basis collocation algorithm was set up to simulate nonlinear dispersive waves propagating in two ways of Boussinesq system by Suárez and Morales [7]. The solutions for three initial boundary value problems modeling motion of single solitary and interaction of solitary waves were demonstrated with the proposed method.…”

Section: Boussinesq Systemsmentioning

confidence: 99%

Exponential B-Splines for Numerical Solutions to Some Boussinesq Systems for Water Waves

2016

View full text Add to dashboard Cite

In the study, the collocation method based on exponential cubic B-spline functions is proposed to solve one dimensional Boussinesq systems numerically. Two initial boundary value problems for Regularized and Classical Boussinesq systems modeling motion of traveling waves are considered. The accuracy of the method is validated by measuring the error between the numerical and analytical solutions. The numerical solutions obtained by various values of free parameter p are compared with some solutions in literature.Keywords: Boussinesq sytems; solitary waves; exponential cubic B-spline; collocation. MSC2010: 35Q99;35C07;76B25;65D07;65M70. Boussinesq SystemsIn the light of the d' Alembert solution, describing two distinct waves moving in the opposite directions for the Cauchy problem for one dimensional wave equation, many physical problems modeled by linear and nonlinear partial differential equations have been solved in wave forms covering traveling waves, solitary waves, harmonic waves, etc. Waves are an important solution class for the model problems in physics, chemistry, and many fields of engineering. This solution type is widely constructed for different models in various media covering solids and fluids. Class of surface bell-shaped solitary waves, having long amplitude when compared with its width, is one of the most prominent classes of waves. In addition to linear equations, solitary wave solutions have also been studied for well known nonlinear equations and systems such as Korteweg-deVries(KdV), Schrödinger, Boussinesq, etc. Having analytical solutions only for some particular cases including additional restrictions and conditions, many numerical methods have been developed to obtain solutions for nonlinear problems. Dougalis et al.[1] studied the numerical behavior of solitary waves of a member of Boussinesq systems family (Bona-Smith system). In that study, long time stability and possible blow-up solutions were examined under small and large perturbations covering perturbation of amplitudes, system coefficients, etc. Numerical models were constructed with the Galerkin-finite element method on the space S h of smooth, periodic, cubic splines. Quintic B-spline collocation tecnique based on Crank-Nicolson formulation was set up for numerical solutions of Boussines type coupled-BBM system [2]. Two initial boundary value problems describing motion of single solitary wave and interaction of solitary waves were simulated by the proposed method. The numerical results were compared with the analytical ones. * Ozlem Ersoy,

show abstract

Numerical Solution of Nonlinear Whitham-Broer-Kaup Shallow Water Model Using Finite Difference Methods

Saeed¹,

Sadeeq²

2017

JZS

View full text Add to dashboard Cite

In this paper, we presented finite difference methods for solving nonlinear Whitham-Broer-Kaup (WBK) shallow water model numerically. We first subdivided the domain of the model by a net with a finite number of mesh points, and the derivative at each point replaced by explicit, Crank-Nicolson, and exponential finite difference approximations. The result is the system of algebraic equations which when solved, provide an approximation to the solutions of WBK model at the selected grid points. Also, a comparison has been made between the approximate solutions obtained by the proposed methods and the exact solutions. Numerical results represented in tables and figures with the help of MATLAB R2015a.

show abstract

Numerical Solutions of Two-Way Propagation of Nonlinear Dispersive Waves Using Radial Basis Functions

Cited by 3 publications

References 18 publications

Numerical Solution of Hirota-satsuma Coupled Kdv System by Rbf-ps Method

Numerical Solution of Hirota-satsuma Coupled Kdv System by Rbf-ps Method

Exponential B-Splines for Numerical Solutions to Some Boussinesq Systems for Water Waves

Numerical Solution of Nonlinear Whitham-Broer-Kaup Shallow Water Model Using Finite Difference Methods

Contact Info

Product

Resources

About