Coiflet solution of strongly nonlinear p-Laplacian equations

doi:10.1007/s10483-017-2212-6

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (7): 1031-1042.doi: https://doi.org/10.1007/s10483-017-2212-6

• 论文 • 上一篇

Coiflet solution of strongly nonlinear p-Laplacian equations

Cong XU, Jizeng WANG, Xiaojing LIU, Lei ZHANG, Youhe ZHOU

Key Laboratory of Mechanics on Disaster and Environment in Western China, the Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China

收稿日期:2016-05-19 修回日期:2016-10-17 出版日期:2017-07-01 发布日期:2017-07-01
通讯作者: Jizeng WANG, E-mail:jzwang@lzu.edu.cn E-mail:jzwang@lzu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Nos. 11472119 and 11421062)

Coiflet solution of strongly nonlinear p-Laplacian equations

Cong XU, Jizeng WANG, Xiaojing LIU, Lei ZHANG, Youhe ZHOU

Key Laboratory of Mechanics on Disaster and Environment in Western China, the Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou 730000, China

Received:2016-05-19 Revised:2016-10-17 Online:2017-07-01 Published:2017-07-01
Contact: Jizeng WANG E-mail:jzwang@lzu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11472119 and 11421062)

摘要/Abstract

摘要：

A new boundary extension technique based on the Lagrange interpolating polynomial is proposed and used to solve the function approximation defined on an interval by a series of scaling Coiflet functions, where the coefficients are used as the single-point samplings. The obtained approximation formula can exactly represent any polynomials defined on the interval with the order up to one third of the length of the compact support of the adopted Coiflet function. Based on the Galerkin method, a Coiflet-based solution procedure is established for general two-dimensional p-Laplacian equations, following which the equations can be discretized into a concise matrix form. As examples of applications, the proposed modified wavelet Galerkin method is applied to three typical p-Laplacian equations with strong nonlinearity. The numerical results justify the efficiency and accuracy of the method.

关键词: discrete variables, structural optimization, combinatorial optimization, local optimum solution, wavelet Galerkin method, boundary extension, p-Laplacian equation, Coiflet

Abstract:

Key words: discrete variables, structural optimization, combinatorial optimization, local optimum solution, wavelet Galerkin method, boundary extension, p-Laplacian equation, Coiflet

中图分类号:

35K05

Cong XU, Jizeng WANG, Xiaojing LIU, Lei ZHANG, Youhe ZHOU. Coiflet solution of strongly nonlinear p-Laplacian equations[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(7): 1031-1042.

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Coiflet solution of strongly nonlinear p-Laplacian equations

Coiflet solution of strongly nonlinear p-Laplacian equations

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