相关论文: Applications of integral transforms composition me…

We present a direct Poisson solver for massively parallel simulations on three-dimensional Cartesian grids with non-uniform spacing. The method uses a tensor-based formulation in which the operator is diagonalized numerically along two…

We propose an efficient method for demodulation of phase modulated signals via iterated Hilbert transform embeddings. We show that while a usual approach based on one application of the Hilbert transform provides only an approximation to a…

This paper is presented to give numerical solutions of some cases of nonlinear wave-like equations with variable coefficients by using Reduced Differential Transform Method (RDTM). RDTM can be applied most of the physical, engineering,…

A method for computing the Hankel transform is proposed whereby the letter is reduced to a sum by representing the integrand as a smooth function times a Bessel function. The smooth function is replaced by its wavelet decomposition with a…

A new development of the ``monodromy transform'' method for analysis of hyperbolic as well as elliptic integrable reductions of Einstein equations is presented. Compatibility conditions for some alternative representations of the…

We review recent progress towards the solution of exactly solved isotropic vertex models with arbitrary toroidal boundary conditions. Quantum space transformations make it possible the diagonalization of the corresponding transfer matrices…

Recently there has been a growing interest in computational methods for quantum scattering equations that avoid the traditional decomposition of wave functions and scattering amplitudes into partial waves.The aim of the present work is to…

In a recent article the authors showed that the radiative Transfer equations with multiple frequencies and scattering can be formulated as a nonlinear integral system. In the present article, the formulation is extended to handle reflective…

We present quadrature schemes to calculate matrices, where the so-called modified Hilbert transformation is involved. These matrices occur as temporal parts of Galerkin finite element discretizations of parabolic or hyperbolic problems when…

A novel technique to determine invariant curves in nonlinear beam dynamics based on the method of formal series has been developed. It is first shown how the solution of the Hamilton equations of motion describing nonlinear betatron…

Surface integral equation (SIE) methods are of great interest for the efficient electromagnetic modeling of various devices, from integrated circuits to antenna arrays. Existing acceleration algorithms for SIEs, such as the adaptive…

Differintegral methods, currently exploited in calculus, provide a fairly unexhausted source of tools to be applied to a wide class of problems involving the theory of special functions and not only. The use of integral transforms of Borel…

Integro-differential methods, currently exploited in calculus, provide an inexhaustible source of tools to be applied to a wide class of problems, involving the theory of special functions and other subjects. The use of integral transforms…

The Calder\'on formulas (i.e., the combination of single-layer and hyper-singular boundary integral operators) have been widely utilized in the process of constructing valid boundary integral equation systems which could possess highly…

A general program to show quantum-classical correspondence for bound conservative integrable and chaotic systems is described. The method is applied to integrable systems and the nature of the approach to the classical limit, the…

A concise method of deriving expressions for Gaussian-like solutions of the paraxial and d'Alembert equations is presented. This method is based on the Hankel transform. Choosing some Gaussian base functions with slight modifications of the…

We propose a method for integrating the right-invariant geodesic flows on Lie groups based on the use of a special canonical transformation in the cotangent bundle of the group. We also describe an original method of constructing exact…

In the frame of the traditional wavelet-Galerkin method based on the compactly supported wavelets, it is important to calculate the so-called connection coefficients that are some integrals whose integrands involve products of wavelets,…

Efficient long-time integration of nonlinear fractional differential equations is significantly challenging due to the integro-differential nature of the fractional operators. In addition, the inherent non-smoothness introduced by the…

We present a Fukushima type decomposition in the setting of general quasi-regular semi-Dirichlet forms. The decomposition is then employed to give a transformation formula for martingale additive functionals. Applications of the results to…