A New Functional Iterative Algorithm for the Regularized Long-Wave Equation Using an Integral Equation Formalism

A New Functional Iterative Algorithm for the Regularized Long-Wave Equation Using an Integral... A fundamental question in computational nonlinear partial differential equations is raised to discover if one could construct a functional iterative algorithm for the regularized long-wave (RLW) equation (or the Benjamin–Bona–Mahony equation) based on an integral equation formalism? Here, the RLW equation is a third-order nonlinear partial differential equation, describing physically nonlinear dispersive waves in shallow water. For the question, the concept of pseudo-parameter, suggested by Jang (Commun Nonlinear Sci Numer Simul 43:118–138, 2017), is introduced and incorporated into the RLW equation. Thereby, dual nonlinear integral equations of second kind involving the parameter are formulated. The application of the fixed point theorem to the integral equations results in a new (semi-analytic and derivative-free) functional iteration algorithm (as required). The new algorithm allows the exploration of new regimes of pseudo-parameters, so that it can be valid for a much wider range (in the complex plane) of pseudo-parameter values than that of Jang (2017). Being fairly simple (or straightforward), the iteration algorithm is found to be not only stable but accurate. Specifically, a numerical experiment on a solitary wave is performed on the convergence and accuracy of the iteration for various complex values of the pseudo-parameters, further providing the regions of convergence subject to some constraints in the complex plane. Moreover, the algorithm yields a particularly relevant physical investigation of the nonlinear behavior near the front of a slowly varying wave train, in which, indeed, interesting nonlinear wave features are demonstrated. As a consequence, the preceding question may be answered. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Scientific Computing Springer Journals

A New Functional Iterative Algorithm for the Regularized Long-Wave Equation Using an Integral Equation Formalism

Loading next page...
 
/lp/springer_journal/a-new-functional-iterative-algorithm-for-the-regularized-long-wave-wT1MKOnYVn
Publisher
Springer Journals
Copyright
Copyright © 2017 by The Author(s)
Subject
Mathematics; Algorithms; Computational Mathematics and Numerical Analysis; Mathematical and Computational Engineering; Theoretical, Mathematical and Computational Physics
ISSN
0885-7474
eISSN
1573-7691
D.O.I.
10.1007/s10915-017-0533-5
Publisher site
See Article on Publisher Site

Abstract

A fundamental question in computational nonlinear partial differential equations is raised to discover if one could construct a functional iterative algorithm for the regularized long-wave (RLW) equation (or the Benjamin–Bona–Mahony equation) based on an integral equation formalism? Here, the RLW equation is a third-order nonlinear partial differential equation, describing physically nonlinear dispersive waves in shallow water. For the question, the concept of pseudo-parameter, suggested by Jang (Commun Nonlinear Sci Numer Simul 43:118–138, 2017), is introduced and incorporated into the RLW equation. Thereby, dual nonlinear integral equations of second kind involving the parameter are formulated. The application of the fixed point theorem to the integral equations results in a new (semi-analytic and derivative-free) functional iteration algorithm (as required). The new algorithm allows the exploration of new regimes of pseudo-parameters, so that it can be valid for a much wider range (in the complex plane) of pseudo-parameter values than that of Jang (2017). Being fairly simple (or straightforward), the iteration algorithm is found to be not only stable but accurate. Specifically, a numerical experiment on a solitary wave is performed on the convergence and accuracy of the iteration for various complex values of the pseudo-parameters, further providing the regions of convergence subject to some constraints in the complex plane. Moreover, the algorithm yields a particularly relevant physical investigation of the nonlinear behavior near the front of a slowly varying wave train, in which, indeed, interesting nonlinear wave features are demonstrated. As a consequence, the preceding question may be answered.

Journal

Journal of Scientific ComputingSpringer Journals

Published: Sep 8, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off