相关论文: Sinc-based method for an efficient solution in the…
We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…
This paper presents a fully discrete numerical scheme for one-dimensional nonlocal wave equations and provides a rigorous theoretical analysis. To facilitate the spatial discretization, we introduce an auxiliary variable analogous to the…
In this work, we investigate numerical solutions of the two-dimensional shallow water wave using a fully nonlinear Green-Naghdi model with an improved dispersive effect. For the purpose of numerics, the Green-Naghdi model is rewritten into…
We solve explicitly the shifted wave equation on Damek--Ricci spaces, using Asgeirsson's theorem and the inverse dual Abel transform. As an application, we investigate Huygens' principle. A similar analysis is carried out in the discrete…
We investigate using plane fronted gravitational wave space-times as model systems to study loop quantization techniques and dispersion relations. In this classical analysis, we start with planar symmetric space-times in the real connection…
We propose an improvement of the basis for the solution of the stationary two-centre Dirac equation in Cassini coordinates using the finite-basis-set method presented in Ref. [1]. For the calculations in Ref. [1], we constructed the basis…
In this paper, we consider a variational formulation for the Dirichlet problem of the wave equation with zero boundary and initial conditions, where we use integration by parts in space and time. To prove unique solvability in a subspace of…
We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…
In this paper, we propose a decomposition approach for eigenvalue problems with spatial symmetries, including the formulation, discretization as well as implementation. This approach can handle eigenvalue problems with either Abelian or…
The group theoretical approach to the relativistic wave equations in the de Sitter and Anti-de Sitter spaces for spin~0 and 1/2 massive particles is considered. The invariant wave equations which determines the appropriate irreducible…
We show that it is possible to obtain numerical solutions to quantum mechanical problems involving a fractional Laplacian, using a collocation approach based on Little Sinc Functions (LSF), which discretizes the Schr\"odinger equation on a…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
In this work, a fully implicit numerical approach based on space-time finite element method is presented to solve the Dirac equation in 1 (space) + 1 (time), 2 + 1, and 3 + 1 dimensions. We utilize PETSc/Tao library to implement our linear…
The Bernstein polynomial basis sees significant use owing to its unique properties, particularly in the field of optimal control. However, the basis is known to have a slow rate of convergence to the function it approximates. With this in…
We solve the inverse problems to recover Dirac systems on an interval or semiaxis from their spectral functions (matrix valued functions) for the case of locally square-integrable potentials. Direct problems in terms of spectral functions…
We rewrite the 1+1 Dirac equation in light cone coordinates in two significant forms, and solve them exactly using the classical calculus of finite differences. The complex form yields ``Feynman's Checkerboard''---a weighted sum over…
To compute the spatially distributed dielectric constant from the backscattering data, we study a coefficient inverse problem for a 1D hyperbolic equation. To solve the inverse problem, we establish a new version of Carleman estimate and…
It is shown that the known method to solve the Dirac equation by means of the squaring method, when relying on the scalar function of the form \Phi = e^{-i\epsilon t} e^{ik_{1} x} e^{ik_{2} y} \sin (kz + \alpha) leads to a 4-dimensional…
The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the…
We propose a meshless conservative Galerkin method for solving Hamiltonian wave equations. We first discretize the equation in space using radial basis functions in a Galerkin-type formulation. Differ from the traditional RBF Galerkin…