Coiflet solution of strongly nonlinear p-Laplacian equations

doi:10.1007/s10483-017-2212-6

Abstract

Abstract:

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.

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

2010 MSC Number:

35K05

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

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