کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
512455 | 866409 | 2013 | 14 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: A meshfree method for the solution of two-dimensional cubic nonlinear Schrödinger equation A meshfree method for the solution of two-dimensional cubic nonlinear Schrödinger equation](/preview/png/512455.png)
In this paper, an efficient numerical technique is developed to approximate the solution of two-dimensional cubic nonlinear Schrödinger equations. The method is based on the nonsymmetric radial basis function collocation method (Kansa's method), within an operator Newton algorithm. In the proposed process, three-dimensional radial basis functions (especially, three-dimensional Multiquadrics (MQ) and Inverse multiquadrics (IMQ) functions) are used as the basis functions. For solving the resulting nonlinear system, an algorithm based on the Newton approach is constructed and applied. In the multilevel Newton algorithm, to overcome the instability of the standard methods for solving the resulting ill-conditioned system an interesting and efficient technique based on the Tikhonov regularization technique with GCV function method is used for solving the ill-conditioned system. Finally, the presented method is used for solving some examples of the governing problem. The comparison between the obtained numerical solutions and the exact solutions demonstrates the reliability, accuracy and efficiency of this method.
Journal: Engineering Analysis with Boundary Elements - Volume 37, Issue 6, June 2013, Pages 885–898