Related papers: Double Fuzzy Complex EE Transform to Solve Partial…
Electrostatic correlations and fluctuations in ionic systems can be described within an extended Poisson-Boltzmann theory using a Gaussian variational form. The resulting equations are challenging to solve because they require the solution…
This paper develops and analyzes an efficient numerical method for solving elliptic partial differential equations, where the diffusion coefficients are random perturbations of deterministic diffusion coefficients. The method is based upon…
We consider the numerical approximation of the radiative transfer equation using discontinuous angular and continuous spatial approximations for the even parts of the solution. The even-parity equations are solved using a diffusion…
Broadly speaking, the calculation of core spectra such as electron energy loss spectra (EELS) at the level of density functional theory (DFT) usually relies one of two approaches: conceptually more complex but computationally efficient…
Partial differential equations (PDEs) play a central role in describing many physical phenomena. Various scientific and engineering applications demand a versatile and differentiable PDE solver that can quickly generate solutions with…
The numerical solution of implicit and stiff differential equations by implicit numerical integrators has been largely investigated and there exist many excellent efficient codes available in the scientific community, as Radau5 (based on a…
In this study, perturbation-iteration algorithm, namely PIA, is applied to solve some types of system of fractional differential equations (FDEs) for the first time. To illustrate the efficiency of the method, numerical solutions are…
Approximate methods have been considered as a means to the evaluation of discrete transforms. In this work, we propose and analyze a class of integer transforms for the discrete Fourier, Hartley, and cosine transforms (DFT, DHT, and DCT),…
One of the major challenges of contemporary mathematics is numerical solving of various problems for functional differential equations (FDE), in particular Cauchy problem for delayed and neutral differential equations. Recently large…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
In this article, we study the ergodicity of neutral retarded stochastic functional differential equations driven by $\alpha$-regular Volterra process. Based on the equivalence between neutral retarded stochastic functional differential…
In this paper, we study the concept of complex fuzzy soft matrices. The application of complex fuzzy soft matrices in signals and systems via the cross product of complex fuzzy soft matrices and Fourier transform was carried out. In this…
We establish new weak existence results for $d$-dimensional Stochastic Volterra Equations (SVEs) with continuous coefficients and possibly singular one-dimensional non-convolution kernels. These results are obtained by introducing an…
Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature problems that may…
We consider the numerical solution of the real time equilibrium Dyson equation, which is used in calculations of the dynamical properties of quantum many-body systems. We show that this equation can be written as a system of coupled,…
We propose a method of solving partial differential equations on the $n$-dimen\-sional unit sphere with methods based on the continuous wavelet transform derived from approximate identities.
It is shown here that the Exact Exchange (EE) formalism provides a natural and rigorous approach for a Density Functional Theory (DFT) of the Integer Quantum Hall Effect (IQHE). Application of a novel EE method to a quasi two-dimensional…
We establish an explicit expression for the conditional Laplace transform of the integrated Volterra Wishart process in terms of a certain resolvent of the covariance function. The core ingredient is the derivation of the conditional…
Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown…
We come back to the Cauchy integral equations occurring in radiative transfer problems posed in finite, plane-parallel media with light scattering taken as monochromatic and isotropic. Their solution is calculated following the classical…