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A Coiflet Wavelet Homotopy Technique for Nonlinear PDEs: Application to the Extreme Bending of Orthotropic Plate with Forced Boundary Constraints
Qiang Yu, Shuaimin Wang, Junfeng Xiao and Hang Xu

Adv. Appl. Math. Mech. DOI: 10.4208/aamm.OA-2022-0214

Publication Date : 2023-02-14

  • 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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