Related papers: New wavelet method based on Shifted Lucas polynomi…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second--order linear partial differential equations, which are admissible potentially…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
In this article, we introduce a new class of coupled fractional Lane-Emden boundary value problems. We employ a novel approach, the fractional Haar wavelet collocation method with the Newton-Raphson method. We analyze the conditions in two…
In the present paper, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on 2-parameters weight functions. Such classes englobe the well…
This paper presents an innovative approach, the Adaptive Orthogonal Basis Method, tailored for computing multiple solutions to differential equations characterized by polynomial nonlinearities. Departing from conventional practices of…
For describing the probability distribution of the positions and times of particles performing anomalous motion, fractional PDEs are derived from the continuous time random walk models with waiting time distribution having divergent first…
We prove that certain polynomials previously introduced by the author can be identified with tau functions of Painlev\'e VI, obtained from one of Picard's algebraic solutions by acting with a four-dimensional lattice of B\"acklund…
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 variational wavelet approach for loops,…
We introduce a new class of polynomials of multiple orthogonality with respect to the product of $r$ classical discrete weights on integer lattices with noninteger shifts. We give explicit representations in the form of the Rodrigues…
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 propose a new adaptive wavelet denoising methodology using complex wavelets. The method is based on a fully Bayesian hierarchical model in the complex wavelet domain that uses a bivariate mixture prior on the wavelet…
Using elementary methods, we establish old and new relations between binomial coefficients, Fibonacci numbers, Lucas numbers, and more.
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 the present work, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of new monogenic polynomials are provided based on 2-parameters weight functions. Such classes extend the well…
Variational inference (VI) has become a widely used approach for scalable Bayesian inference, but its performance strongly depends on the flexibility of the chosen variational family. In this work, we propose a novel variational family that…
A high precision, and space time fully decoupled, wavelet formulation numerical method is developed for a class of nonlinear initial boundary value problems. This method is established based on a proposed Coiflet based approximation scheme…
We present algorithms to numerically evaluate Daubechies wavelets and scaling functions to high relative accuracy. These algorithms refine the suggestion of Daubechies and Lagarias to evaluate functions defined by two-scale difference…
This article provides an effective computational algorithm based on Legendre wavelet (LW) and standard tau approach to approximate the solution of multi-dimensional distributed order time-space fractional weakly singular integro-partial…
The Differential Transfer Matrix Method is extended to the complex plane, which allows dealing with singularities at turning points. The result for real-valued systems are simplified and a pair of basis functions is found. These bases are a…