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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

    CMES-Computer Modeling in Engineering & Sciences, Vol.44, No.2, pp. 115-136, 2009, DOI: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. More >

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