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

Sirajul Haq1,2, Siraj-Ul-Islam3, Marjan Uddin1,4
Faculty of Engineering Sciences, GIK Institute, Topi 23640, NWFP, Pakistan
siraj_jcs@yahoo.co.in (corresponding author)
University of Engineering and Technology, Peshawar, NWFP, Pakistan. siraj.islam@gmail.com
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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Cite This Article

Haq, S., , S., Uddin, M. (2009). Numerical Solution of Nonlinear Schrodinger Equations by Collocation Method Using Radial Basis Functions. CMES-Computer Modeling in Engineering & Sciences, 44(2), 115–136.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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