Wavelets of Wilson Type with Arbitrary Shapes

Wilson wavelets for solving nonlinear stochastic integral equations

A new computational method based on Wilson wavelets is proposed for solving a class of nonlinear stochastic It^{o}-Volterra integral equations. To do this a new stochastic operational matrix of It^{o} integration for Wilson wavelets is obtained. Block pulse functions (BPFs) and collocation method are used to generate a process to forming this matrix. Using these basis functions and their operat...

Anisotropic zero-index waveguide with arbitrary shapes

We design a series of waveguides composed of uniform anisotropic epsilon-near-zero media. Unlike normal waveguides in which the transmission rate strongly depends on the width and the boundary shape, such waveguides can achieve high transmission with almost arbitrary width and boundary shapes, leading to applications such as unusual waveguides, wave expanders and compressors, splitters, bends, ...

Wave Scattering by Small Bodies of Arbitrary Shapes. Wave Scattering by Small Bodies of Arbitrary Shapes * †

Construction of multivariate biorthogonal wavelets with arbitrary vanishing moments

We present a concrete method to build discrete biorthogonal systems such that the wavelet filters have any number of vanishing moments. Several algorithms are proposed to construct multivariate biorthogonal wavelets with any general dilation matrix and arbitrary order of vanishing moments. Examples are provided to illustrate the general theory and the advantages of the algorithms. §

Application of Daubechies wavelets for solving Kuramoto-Sivashinsky‎ type equations

We show how Daubechies wavelets are used to solve Kuramoto-Sivashinsky type equations with periodic boundary condition‎. ‎Wavelet bases are used for numerical solution of the Kuramoto-Sivashinsky type equations by Galerkin method‎. ‎The numerical results in comparison with the exact solution prove the efficiency and accuracy of our method‎.