کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
9662292 | 698771 | 2005 | 18 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Radial point interpolation collocation method (RPICM) for partial differential equations
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موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
علوم کامپیوتر (عمومی)
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
This paper presents a truly meshfree method referred to as radial point interpolation collocation method (RPICM) for solving partial differential equations. This method is different from the existing point interpolation method (PIM) that is based on the Galerkin weak-form. Because it is based on the collocation scheme no background cells are required for numerical integration. Radial basis functions are used in the work to create shape functions. A series of test examples were numerically analysed using the present method, including 1-D and 2-D partial differential equations, in order to test the accuracy and efficiency of the proposed schemes. Several aspects have been numerically investigated, including the choice of shape parameter c with can greatly affect the accuracy of the approximation; the enforcement of additional polynomial terms; and the application of the Hermite-type interpolation which makes use of the normal gradient on Neumann boundary for the solution of PDEs with Neumann boundary conditions. Particular emphasis was on an efficient scheme, namely Hermite-type interpolation for dealing with Neumann boundary conditions. The numerical results demonstrate that good improvement on accuracy can be obtained after using Hermite-type interpolation. The h-convergence rates are also studied for RPICM with different forms of basis functions and different additional terms.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Computers & Mathematics with Applications - Volume 50, Issues 8â9, OctoberâNovember 2005, Pages 1425-1442
Journal: Computers & Mathematics with Applications - Volume 50, Issues 8â9, OctoberâNovember 2005, Pages 1425-1442
نویسندگان
X. Liu, G.R. Liu, K. Tai, K.Y. Lam,