A Fully Implicit Finite Difference Approach for Numerical Solution of the Generalized Equal Width (GEW) Equation

In this paper, a fully implicit finite difference method is presented to solve the generalized equal width equation. This implicit method allows to handle any values of p . Since the equation is nonlinear the scheme leads to a system of nonlinear equations. At each time step, Newton’s method is used...

Full description

Saved in:
Bibliographic Details
Published in:Proceedings of the National Academy of Sciences, India, Section A, physical sciences India, Section A, physical sciences, 2020-06, Vol.90 (2), p.299-308
Main Authors: Inan, Bilge, Bahadir, Ahmet Refik
Format: Article
Language:English
Subjects:
Applied and Technical Physics
Atomic
Finite difference method
Mathematical analysis
Molecular
Nonlinear equations
Nonlinear systems
Optical and Plasma Physics
Physics
Physics and Astronomy
Quantum Physics
Research Article
Stability analysis
Viscosity
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, a fully implicit finite difference method is presented to solve the generalized equal width equation. This implicit method allows to handle any values of p . Since the equation is nonlinear the scheme leads to a system of nonlinear equations. At each time step, Newton’s method is used to solve this nonlinear system. The linear stability analysis of the proposed method is investigated using von Neumann approach and at the end of this investigation is seen that the method is unconditionally stable. The results are comparisons with analytical and other numerical values clearly show that results obtained using the fully implicit finite difference scheme are precise and reliable.
ISSN:0369-8203
2250-1762
DOI:10.1007/s40010-019-00594-8