A new functional iterative algorithm for the regularized long-wave equation using an integral equation formalism
type: Item
instance of: scholarly article
title: A new functional iterative algorithm for the regularized long-wave equation using an integral equation formalism
zbMATH Open document ID: 1408.65104
published in: Journal of Scientific Computing
publication date: 2018-04-13T00:00:00Z
review text: The author investigates the third-order nonlinear partial differential equation \( \eta_{t} + c_{0}\eta_{x} + \frac{3c_{0}}{2h_{0}}\eta\eta_{x} - \frac{h_{0}^{2}}{6}\eta_{xxt} = 0 \), describing some class of waves in shallow water. Here, \(\eta\) denotes the wave elevation and the other values describe physical characteristics of the process. It is proved that the solution of this equation (together with some initial conditions) satisfies a system of nonlinear integral equations. If the corresponding integral operator acting in some Banach space is contractive, then the classical iterative process permits to obtain solutions of the differential equation under consideration. The paper contains results of numerous computational experiments.
reviewed by: Vladimir S. Pilidi
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 65R10
Mathematics Subject Classification ID: 35C08
Mathematics Subject Classification ID: 76B15
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 35Q86
Mathematics Subject Classification ID: 86A05
zbMATH DE Number: 6859533
zbMATH Keywords: regularized long-wave (RLW) equation
zbMATH Keywords: pseudo-parameter
zbMATH Keywords: nonlinear integral equations of second kind
zbMATH Keywords: contractive operator
zbMATH Keywords: functional iteration algorithm
author: T. S. Jang
Wikidata QID: Q59513420
MaRDI profile type: Publication
full work available at URL: s10915-017-0533-5
OpenAlex ID: W2753085900
cites work: Q4151274
cites work: Model equations for long waves in nonlinear dispersive systems
cites work: Approximation of the RLW equation by the least square cubic \(B\)-spline finite element method
cites work: Numerical study of the regularized long-wave equation. II: Interaction of solitary waves
cites work: A computational method for regularized long wave equation
cites work: Multisymplectic numerical method for the regularized long-wave equation
cites work: A B‐spline finite element method for the regularized long wave equation
cites work: Application of cubic B-splines for numerical solution of the RLW equation
cites work: A new dispersion-relation preserving method for integrating the classical Boussinesq equation
cites work: Q4108257
cites work: Q4158998
cites work: A Petrov-Galerkin finite element scheme for the regularized long wave equation
cites work: Parametric spline solution of the regularized long wave equation
cites work: Numerical solutions of RLW equation using Galerkin method with extrapolation techniques
cites work: A least-squares finite element scheme for the RLW equation
cites work: Numerical solution of RLW equation using linear finite elements within Galerkin's method
cites work: A computational method for the regularized long wave (RLW) equation
cites work: Galerkin method for the numerical solution of the RLW equation using quintic B-splines
cites work: B-Spline Collocation Methods For Numerical Solutions Of The Rlw Equation
cites work: A collocation method with cubic B-splines for solving the MRLW equation
DOI: 10.1007/S10915-017-0533-5
Recommended article: A computational method for regularized long wave equation
Recommended article: Application of the variational iteration method to the regularized long wave equation
Recommended article: Q3113903
Recommended article: A computational method for the regularized long wave (RLW) equation
Recommended article: A finite difference scheme for generalized regularized long-wave equation
Recommended article: Two efficient methods for solving the generalized regularized long wave equation
Recommended article: Some linearly and non-linearly implicit schemes for the numerical solutions of the regularized long-wave equation
Recommended article: A finite difference solution of the regularized long-wave equation
Recommended article: Q3017794
Recommended article: A Numerical Method for the Generalized Regularized Long Wave Equation Using a Reproducing Kernel Function
description: scientific article; zbMATH DE number 6859533