Harmonic wavelet analysis of nonlinear waves

A method based on a multiscale (wavelet) decomposition is proposed for the analysis of nonlinear waves in hyperelastic materials. The wave solution is approximated by a discrete series expansion with respect to the harmonic wavelets, and it is compared with the solution obtained by the method of successive approximations

Harmonic Wavelet Analysis of Nonlinear Waves

A method based on a multiscale (wavelet) decomposition is proposed for the analysis of nonlinear waves inhyperelastic materials. The wave solution is approximated by a discrete series expansion with respect to the harmonic wavelets, and it is compared with the solution obtained by the method of successive approximations

Modified hierarchy basis for solving singular boundary value problems

AbstractIn this paper, we develop an efficient preconditioning method on the basis of the modified hierarchy basis for solving the singular boundary value problem by the Galerkin method. After applying the preconditioning method, we show that the condition number of the linear system arising from the Galerkin method is uniformly bounded. In particular, the condition number of the preconditioned system will be bounded by 2 for the case q(x)=0 (see Eq. (1) in the paper). Numerical results are presented to confirm our theoretical results