A wavelet-based method with arbitrary high order of accuracy for nonlinear problems in mechanics

Abstract eng:
A high-order wavelet-based solution method is developed for general nonlinear boundary value problems in mechanics. This method is established based on a Coiflet (a typical wavelet) approximation of n-tuple integrals of interval bounded functions combined with an accurate and adjustable boundary extension technique. Accuracy order of the proposed method is proven to be any positive even number N as long as the Coiflet with N vanishing moment is adopted. And most interestingly, this accuracy is independent of the highest order of derivatives in the equation to be solved. Error analysis and numerical examples of a wide range of nonlinear mechanical problems have demonstrate that the proposed wavelet method has a much better accuracy and efficiency than most major existing methods.

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