Open Access

ARTICLE

Numerical Solution of Nonlinear Schrodinger Equations by Collocation Method Using Radial Basis Functions

Sirajul Haq^1,2, Siraj-Ul-Islam³, Marjan Uddin^1,4

1 Faculty of Engineering Sciences, GIK Institute, Topi 23640, NWFP, Pakistan
2 siraj_jcs@yahoo.co.in (corresponding author)
3 University of Engineering and Technology, Peshawar, NWFP, Pakistan. siraj.islam@gmail.com
4 marjankhan1@hotmail.com

Computer Modeling in Engineering & Sciences 2009, 44(2), 115-136. https://doi.org/10.3970/cmes.2009.044.115

Abstract

A mesh free method for the numerical solution of the nonlinear Schrodinger (NLS) and coupled nonlinear Schrodinger (CNLS) equation is implemented. The presented method uses a set of scattered nodes within the problem domain as well as on the boundaries of the domain along with approximating functions known as radial basis functions (RBFs). The set of scattered nodes do not form a mesh, means that no information of relationship between the nodes is needed. Error norms L₂, L_∞ are used to estimate accuracy of the method. Stability analysis of the method is given to demonstrate its practical applicability.

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Keywords

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