کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8900564 | 1631717 | 2018 | 12 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Reproducing kernel method for the numerical solution of the 1D Swift-Hohenberg equation
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Reproducing kernel method for the numerical solution of the 1D Swift-Hohenberg equation Reproducing kernel method for the numerical solution of the 1D Swift-Hohenberg equation](/preview/png/8900564.png)
چکیده انگلیسی
The Swift-Hohenberg equation is a nonlinear partial differential equation of fourth order that models the formation and evolution of patterns in a wide range of physical systems. We study the 1D Swift-Hohenberg equation in order to demonstrate the utility of the reproducing kernel method. The solution is represented in the form of a series in the reproducing kernel space, and truncating this series representation we obtain the n-term approximate solution. In the first approach, we aim to explain how to construct a reproducing kernel method without using Gram-Schmidt orthogonalization, as orthogonalization is computationally expensive. This approach will therefore be most practical for obtaining numerical solutions. Gram-Schmidt orthogonalization is later applied in the second approach, despite the increased computational time, as this approach will prove theoretically useful when we perform a formal convergence analysis of the reproducing kernel method for the Swift-Hohenberg equation. We demonstrate the applicability of the method through various test problems for a variety of initial data and parameter values.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Mathematics and Computation - Volume 339, 15 December 2018, Pages 132-143
Journal: Applied Mathematics and Computation - Volume 339, 15 December 2018, Pages 132-143
نویسندگان
P. Bakhtiari, S. Abbasbandy, R.A. Van Gorder,