Paper Info
Title
Numerical investigation based on direct meshless local Petrov Galerkin (direct MLPG) method for solving generalized Zakharov system in one and two dimensions and generalized Gross-Pitaevskii equation.
Abstract
In the current investigation, we propose two efficient meshless numerical techniques for solving two models in optic engineering, i.e. the generalized Gross–Pitaevskii equation and the generalized Zakharov system. Two local meshless methods have been employed for solving these models: local radial basis functions collocation method and direct meshless local Petrov–Galerkin method. In this paper, we discrete the space direction using the local radial basis functions collocation and direct meshless local Petrov–Galerkin techniques and to obtain high-order numerical results, we use the fourth-order exponential time differencing Runge–Kutta method for discretizing the temporal direction. The obtained numerical results are compared with some well-known numerical techniques. Moreover, several examples are given that show the acceptable accuracy and efficiency of the proposed scheme.
Year
DOI
Venue
2017
10.1007/s00366-017-0510-5
Eng. Comput. (Lond.)
Keywords
Field
DocType
Meshless method, Direct meshless local Petrov–Galerkin (DMLPG) method, Local radial basis functions collocation method, The generalized Gross–Pitaevskii equation, The generalized Zakharov system, Fourth-order exponential time differencing Runge–Kutta method
Zakharov system,Discretization,Mathematical optimization,Meshfree methods,Mathematical analysis,Galerkin method,Singular boundary method,Basis function,Collocation method,Mathematics,Regularized meshless method
Journal
Volume
Issue
ISSN
33
4
0177-0667
Citations 
PageRank 
References 
4
0.44
23
Authors
2
Name
Order
Citations
PageRank
Mehdi Dehghan13022324.48
Mostafa Abbaszadeh221318.53