Related papers: Negative dimensional approach to evaluating real i…
We deal with the higher-order fractional Laplacians by two methods: the integral method and the system method. The former depends on the integral equation equivalent to the differential equation. The latter works directly on the…
Negative dimensional integration method (NDIM) is revealing itself as a very useful technique for computing Feynman integrals, massless and/or massive, covariant and non-covariant alike. Up to now, however, the illustrative calculations…
This paper is devoted to the study of the singularly perturbed second order partial integro-differential equations. The estimation of the solutions of Cauchy problem is obtained.
The goal of this paper is to formalize the notion of The Compositional Integral in The Complex Plane. We prove a convergence theorem guaranteeing its existence. We prove an analogue of Cauchy's Integral Theorem--and suggest an approach at…
We construct the integrals of motion for several models of the quantum damped oscillators in nonrelativistic quantum mechanics in a framework of a general approach to the time-dependent Schroedinger equation with variable quadratic…
We consider a class of equations with the fractional differentiation operator $D^\alpha$, $\alpha >0$, for complex-valued functions $x\mapsto f(|x|_K)$ on a non-Archimedean local field $K$ depending only on the absolute value $|\cdot |_K$.…
Phase retrieval problems occur in a width range of applications in physics and engineering such as crystallography, astronomy, and laser optics. Common to all of them is the recovery of an unknown signal from the intensity of its Fourier…
Two new methods of numerical integration of Cauchy problems for ODEs with blow-up solutions are described. The first method is based on applying a differential transformation, where the first derivative (given in the original equation) is…
A formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad…
We provide a simple approach for the evaluation of inverse integral transforms that does not require any knowledge of complex analysis. The central idea behind the method is to reduce the inverse transform to the solution of an ordinary…
We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…
In this paper, we study the class of one dimensional singular integrals that converge in the sense of Cauchy principal value. In addition, we present a simple method for approximating such integrals.
When a Monte Carlo algorithm is used to evaluate a physical observable A, it is possible to slightly modify the algorithm so that it evaluates simultaneously A and the derivatives $\partial$ $\varsigma$ A of A with respect to each…
The problem of evaluating potential integrals on planar triangular elements has been addressed using a polar coordinate decomposition. The resulting formulae are general, exact, easily implemented, and have only one special case, that of a…
We consider a mechanical system with impact and n degrees of freedom, written in generalized coordinates. The system is not necessarily Lagrangian. The representative point of the system must remain inside a set of constraints K; the…
Negative dimensional integration method (NDIM) seems to be a very promising technique for evaluating massless and/or massive Feynman diagrams. It is unique in the sense that the method simultaneously gives solutions in different regions of…
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…
Parabolic integro-differential nondegenerate Cauchy problem is considered in the scale of L_{p} spaces of functions whose regularity is defined by a Levy measure with O-regulary varying radial profile. Existence and uniqueness of a solution…
The objective of this article is to introduce a novel technique for computing numerical solutions to the nonlinear inverse heat conduction problem. This involves solving nonlinear parabolic equations with Cauchy data provided on one side…
We prove Cauchy's formula for repeated integration on time scales. The obtained relation gives rise to new notions of fractional integration and differentiation on arbitrary nonempty closed sets.