A Coiflet Wavelet Homotopy Technique for Nonlinear PDEs: Application to the Extreme Bending of Orthotropic Plate with Forced Boundary Constraints

A Coiflet Wavelet Homotopy Technique for Nonlinear PDEs: Application to the Extreme Bending of Orthotropic Plate with Forced Boundary Constraints

Year:    2023

Author:    Qiang Yu, Shuaimin Wang, Junfeng Xiao, Hang Xu

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 6 : pp. 1473–1514

Abstract

A generalized homotopy-based Coiflet-type wavelet method for solving strongly nonlinear PDEs with nonhomogeneous edges is proposed. Based on the improvement of boundary difference order by Taylor expansion, the accuracy in wavelet approximation is largely improved and the accumulated error on boundary is successfully suppressed in application. A unified high-precision wavelet approximation scheme is formulated for inhomogeneous boundaries involved in generalized Neumann, Robin and Cauchy types, which overcomes the shortcomings of accuracy loss in homogenizing process by variable substitution. Large deflection bending analysis of orthotropic plate with forced boundary moments and rotations on nonlinear foundation is used as an example to illustrate the wavelet approach, while the obtained solutions for lateral deflection at both smally and largely deformed stage have been validated compared to the published results in good accuracy. Compared to the other homotopy-based approach, the wavelet scheme possesses good efficiency in transforming the differential operations into algebraic ones by converting the differential operators into iterative matrices, while nonhomogeneous boundary is directly approached dispensing with homogenization. The auxiliary linear operator determined by linear component of original governing equation demonstrates excellent approaching precision and the convergence can be ensured by iterative approach.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2022-0214

Advances in Applied Mathematics and Mechanics, Vol. 15 (2023), Iss. 6 : pp. 1473–1514

Published online:    2023-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    42

Keywords:    Wavelet method higher-order interpolating continuation homotopy analysis method geometric nonlinearity orthotropic plate.

Author Details

Qiang Yu

Shuaimin Wang

Junfeng Xiao

Hang Xu

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