Related papers: The solution of multi-scale partial differential e…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider the applications of discrete wavelet analysis…
We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive)…
In this paper, we present a new modified Newton method a use of Haar wavelet formula for solving non-linear equations. This new method do not require the use of the second-order derivative. It is shown that the new method has third-order of…
It is demonstrated that the wavelets can be used to considerably speed up simulations of the wave packet propagation in multiscale systems. Extremely high efficiency is obtained in the representation of both bound and continuum states. The…
Wavelet based algorithms in numerical analysis are similar to other transform methods in that vectors and operators are expanded into a basis and the computations take place in this new system of coordinates. However, due to the recursive…
The aim of this article is to analyze numerical schemes using two-layer neural networks with infinite width for the resolution of the high-dimensional Poisson-Neumann partial differential equations (PDEs) with Neumann boundary conditions.…
We describe a multi-scale resolution approach to analyzing problems in Quantum Mechanics using Daubechies wavelet basis. The expansion of the wavefunction of the quantum system in this basis allows a natural interpretation of each basis…
New elliptic cylindrical wavelets are introduced, which exploit the relationship between analysing filters and Floquet's solution of Mathieu differential equations. It is shown that the transfer function of both multiresolution filters is…
In this paper we discuss the use of wavelet bases to solve the relativistic three-body problem. Wavelet bases can be used to transform momentum-space scattering integral equations into an approximate system of linear equations with a sparse…
We present the applications of variational-wavelet approach for computing multiresolution/multiscale representation for solution of some approximations of Vlasov-Maxwell-Poisson equations.
Classical multiscale analysis based on wavelets has a number of successful applications, e.g. in data compression, fast algorithms, and noise removal. Wavelets, however, are adapted to point singularities, and many phenomena in several…
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part, according to variational approach we obtain a…
In current work, non-familiar shifted Lucas polynomials are introduced. We have constructed a computational wavelet technique for solution of initial/boundary value second order differential equations. For this numerical scheme, we have…
In this paper we explain how to use the Fast Fourier Transform (FFT) to solve partial differential equations (PDEs). We start by defining appropriate discrete domains in coordinate and frequency domains. Then describe the main limitation of…
We present the application of the variational-wavelet analysis to the analysis of quantum ensembles in Wigner framework. (Naive) deformation quantization, the multiresolution representations and the variational approach are the key points.…
We present a high-order spacetime numerical method for discretizing and solving linear initial-boundary value problems using wavelet-based techniques with user-prescribed error estimates. The spacetime wavelet discretization yields a system…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation…
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The…