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In this article I present a fast and direct method for solving several types of linear finite difference equations (FDE) with constant coefficients. The method is based on a polynomial form of the translation operator and its inverse, and…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
In the context of electromagnetism and nonlinear optical interactions damping is generally introduced as a phenomenological, viscous term that dissipates energy, proportional to the temporal derivative of the polarization. Here, we follow…
Background: The numerical solution of few-body scattering problems with realistic interactions is a difficult problem that normally must be solved on powerful supercomputers, taking a lot of computer time. This strongly limits the…
We propose a high-order FDTD scheme based on the correction function method (CFM) to treat interfaces with complex geometry without increasing the complexity of the numerical approach for constant coefficients. Correction functions are…
This article develops how to generalize the invariant subspace method for deriving the analytical solutions of the multi-component (N+1)-dimensional coupled nonlinear time-fractional PDEs (NTFPDEs) in the sense of Caputo fractional-order…
A fundamental issue in classical electrodynamics is represented by the search of the exact equation of motion for a classical charged particle under the action of its electromagnetic (EM) self-field - the so-called radiation-reaction…
The random feature method (RFM) has demonstrated great potential in bridging traditional numerical methods and machine learning techniques for solving partial differential equations (PDEs). It retains the advantages of mesh-free approaches…
We address the problem of collective motion across a barrier like encountered in fission. A formula for the quantal decay rate is derived which bases on a recently developed variational approach for functional integrals. This formula can be…
A system of reduced equations is proposed for the electron motion in the strongly-radiation dominated regime for an arbitrary electromagnetic field configuration. The developed approach is used to analyze various scenarios of an electron…
It is shown that a class of approximate resonance solutions in the three-body problem under the Newtonian gravitational force are equivalent to quantized solutions of a modified Schr\"odinger equation for a wide range of masses that…
Real-time computation of time-dependent quantum mechanical problems are presented for nuclear many-body problems. Quantum tunneling in nuclear fusion at low energy is described using a time-dependent wave packet. A real-time method of…
In this work, based on consideration of periodicity and asymptotic forms of wave function, we propose a novel approach to the solution of finite volume three-body problem by mapping a three-body problem into a higher dimensional two-body…
We present a mimetic finite-difference approach for solving Maxwell's equations in one and two spatial dimensions. After introducing the governing equations and the classical Finite-Difference Time-Domain (FDTD) method, we describe mimetic…
We critically explore the applicability of a recently proposed framework to sample the quantum dynamics of a many-body quantum system interacting with light by stochastic trajectories, applying it to the closed and open Tavis-Cummings model…
Multiphysics systems are driven by multiple processes acting simultaneously, and their simulation leads to partitioned systems of differential equations. This paper studies the solution of partitioned systems of differential equations using…
Motivated by important applications in image processing, we study a class of second-order geometric quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems…
Fractional-order differential equations (FDEs) enhance traditional differential equations by extending the order of differential operators from integers to real numbers, offering greater flexibility in modeling complex dynamical systems…
The Faddeev equation for three-body scattering at arbitrary energies is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. In its simplest form the Faddeev equation…
In this paper we discuss some issues that arise in the process of writing a fractional differential equation (FDE) by replacing an integer order derivative by a fractional order derivative in a given differential equation. To address these…