کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
513229 | 866459 | 2010 | 9 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: The golden section search algorithm for finding a good shape parameter for meshless collocation methods The golden section search algorithm for finding a good shape parameter for meshless collocation methods](/preview/png/513229.png)
In this paper we propose to apply the golden section search algorithm to determining a good shape parameter of multiquadrics (MQ) for the solution of partial differential equations. We use two radial basis function based meshless collocation methods, the method of approximate particular solutions (MAPS) and Kansa's method, to solve partial differential equations. Due to the severely ill-conditioned matrix system using MQ, we also consider the truncated singular value decomposition method (TSVD) to regularize the smoothness of the error versus shape parameter curve so that a reasonably good shape parameter can be identified. We also analyze cost and accuracy for using LU decomposition and TSVD. Numerical results show that the proposed golden section search method is effective and provides a reasonable shape parameter along with acceptable accuracy of the solution.
Journal: Engineering Analysis with Boundary Elements - Volume 34, Issue 8, August 2010, Pages 738–746