Related papers: Double power series method for approximating cosmo…
The Fokker-Planck equation describing the transport of energetic particles interacting with turbulence is difficult to solve analytically. Numerical solutions are of course possible but they are not always useful for applications. In the…
In these lectures we introduce the Feynman-Schwinger representation method for solving nonperturbative problems in field theory. As an introduction we first give a brief overview of integral equations and path integral methods for solving…
We present a rigorous and comprehensive investigation of a generalized inflationary perturbation theory designed to address persistent large-scale anomalies in the Cosmic Microwave Background (CMB). Motivated by the Trans-Planckian problem…
Sextic oscillator in D dimensions is considered as a typical quasi-exactly solvable (QES) model. Usually, its QES N-plets of bound states have to be computed using the coupled Magyari's nonlinear algebraic equations. We propose and describe…
We present the first systematic derivation of the one-loop correction to the large scale matter power spectrum in a mixed cold+hot dark matter cosmology with subdominant massive neutrino hot dark matter. Starting with the equations of…
In this paper, two numerical schemes for a nonlinear integral equation of Fredholm type with weakly singular kernel are proposed. These numerical methods combine sinc-collocation and sinc-convolution approximations with Newton and steepest…
The forward-backward splitting method (FBS) for minimizing a nonsmooth composite function can be interpreted as a (variable-metric) gradient method over a continuously differentiable function which we call forward-backward envelope (FBE).…
Distributed order fractional operators offer a rigorous tool for mathematical modelling of multi-physics phenomena, where the differential orders are distributed over a range of values rather than being just a fixed integer/fraction as it…
We propose the novel numerical scheme for solution of the multidimensional Fokker-Planck equation, which is based on the Chebyshev interpolation and the spectral differentiation techniques as well as low rank tensor approximations, namely,…
We develop a framework for Large Scale Structure (LSS) perturbation theory, that solves the Vlasov-Poisson system of equations for the distribution function in full phase space. This approach relaxes the usual apriori assumption of…
Accurately simulating wave propagation is crucial in fields such as acoustics, electromagnetism, and seismic analysis. Traditional numerical methods, like finite difference and finite element approaches, are widely used to solve governing…
We propose new algorithms for the computation of the first N terms of a vector (resp. a basis) of power series solutions of a linear system of differential equations at an ordinary point, using a number of arithmetic operations which is…
We present a Mathematica package for performing algebraic and numerical computations in cosmological models based on supersymmetric theories. The programs allow for (I) evaluation and study of the properties of a scalar potential in a large…
In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations. The FNN architecture comprises input, middle, and output layers, with various degrees of Fibonacci…
Based on the multi-point propagator expansion, we present resummed perturbative calculations for cosmological power spectra and correlation functions in the context of modified gravity. In a wide class of modified gravity models that have a…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
This work presents an algorithmic scheme for solving the infinite-time constrained linear quadratic regulation problem. We employ an accelerated version of a popular proximal gradient scheme, commonly known as the Forward-Backward Splitting…
We apply polynomial approximation methods -- known in the numerical PDEs context as spectral methods -- to approximate the vector-valued function that satisfies a linear system of equations where the matrix and the right hand side depend on…
The purpose of this study is to utilize the Chebyshev spectral method neural network(CSNN) model to solve differential equations. This approach employs a single-layer neural network wherein Chebyshev spectral methods are used to construct…
A perturbation approach based on the first-order mean spherical approximation (FMSA) is proposed. It consists in adopting a hard-sphere plus short-range attractive Yukawa fluid as the novel reference system, over which the perturbative…