Related papers: Be careful with the Exp-function method
In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…
We propose a new analytical method to solve for nonexactly soluble Schrodinger equation via expansions through some existing quantum numbers. Successfully, it is applied to the rational non-polynomial oscillator potential. Moreover, a…
The derivative expansion approach to the calculation of the interaction between two surfaces, is a generalization of the proximity force approximation, a technique of widespread use in different areas of physics. The derivative expansion…
The method of expansion of integrals in external parameters is suggested. It is quite universal and works for Feynman integrals both in Euclidean and Minkowski regions of momenta.
In [8], some exact splittings are proposed for inhomogeneous quadratic differential equations including, for example, transport equations, kinetic equations, and Schr{\"o}dinger type equations with a rotation term. In this work, these exact…
This article examines a new approach to solving ordinary differential equations based on Fractional-Calculus theory. Poisson and Sturm-Liouville-type problems are studied, together with different boundary conditions. Each case is analyzed…
We develop two numerical methods to solve the differential equations with deviating arguments for the motion of two charges in the action-at-a-distance electrodynamics. Our first method uses St\"urmer's extrapolation formula and assumes…
A method is presented to construct exactly solvable nonlinear extensions of the Schr\"odinger equation. The method explores a correspondence which can be established under certain conditions between exactly solvable ordinary Schr\"odinger…
In this paper, we introduce a new finite expression method (FEX) to solve high-dimensional partial integro-differential equations (PIDEs). This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel…
We address the problem of minimizing a quadratic function subject to linear constraints over binary variables. We introduce the exact solution method called EXPEDIS where the constrained problem is transformed into a max-cut instance, and…
We provide a novel existence result for energy-variational solutions to a general class of evolutionary partial differential equations. Compared to previous works on this solution concept, the generalization is mainly twofold: a relaxation…
An inexact Newton type method for numerical minimization of convex piecewise quadratic functions is considered and its convergence is analyzed. Earlier, a similar method was successfully applied to optimizaton problems arising in numerical…
We introduce a generalized finite difference method for solving a large range of fully nonlinear elliptic partial differential equations in three dimensions. Methods are based on Cartesian grids, augmented by additional points carefully…
The effective properties of composites and review literature on the methods of Rayleigh, Natanzon--Filshtinsky, functional equations and asymptotic approaches are outlined. In connection with the above methods and new recent publications…
We obtain exact solutions to the class of parabolic partial differential equations of arbitrary dimensionality and with arbitrary potentials. The solutions are presented in a compact-form: as explicit mathematical expressions consisting of…
A method for the search of exact solutions for equation of a nonlocal scalar field in a non-flat metric is considered. In the Friedmann-Robertson-Walker metric the proposed method can be used in the case of an arbitrary potential, with the…
We consider a singular fractional differential equation involving generalized Katugampola derivative and obtain the existence and uniqueness of its solution. A scheme for uniformly approximating solution is constructed by using Picard…
Below, the explicit solution to a certain finite-difference equation is given and the required steps for derivation of these results are outlined. Everything is included as Mathematica formulae, so the notebook itself can be used for…
An exact method for direct calculation of the Jost function and Jost solutions for a repulsive singular potential is presented. Within this method the Schrodinger equation is replaced by an equivalent system of linear first-order…
The fundamental importance of functional differential equations has been recognized in many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations)…