Related papers: Barrier penetration in a discrete basis formalism
This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…
The shell model solve the nuclear many-body problem in a restricted model space and takes into account the restricted nature of the space by using effective interactions and operators. In this paper two different methods for generating the…
A singularly perturbed linear system of second order ordinary differential equations of reaction-diffusion type with given boundary conditions is considered. The leading term of each equation is multiplied by a small positive parameter.…
We consider the numerical approximation of the stochastic complex Ginzburg-Landau equation with additive noise on the one dimensional torus. The complex nature of the equation means that many of the standard approaches developed for…
Based on the radial basis function (RBF), non-singular general solution and dual reciprocity principle (DRM), this paper presents an inheretnly meshless, exponential convergence, integration-free, boundary-only collocation techniques for…
For the first time, the general nonlinear Schr\"odinger equation is investigated, in which the chromatic dispersion and potential are specified by two arbitrary functions. The equation in question is a natural generalization of a wide class…
Recent years have seen an increasing amount of research devoted to the development of so-called resonance-based methods for dispersive nonlinear partial differential equations. In many situations, this new class of methods allows for…
The H(div)-conforming approach for the Brinkman equation is studied numerically, verifying the theoretical a priori and a posteriori analysis in previous work of the authors. Furthermore, the results are extended to cover a non-constant…
Several new methods of numerical integration of Cauchy problems with blow-up solutions for nonlinear ordinary differential equations of the first- and second-order are described. Solutions of such problems have singularities whose positions…
A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
A new integrable discrete system is constructed and studied, based on the algebraization of the difference operator. The model is named the discrete generalized nonlinear Schrodinger (GNLS) equation for which can be reduced to classical…
We consider the generalized time-dependent Schr\"odinger equation on the half-axis and a broad family of finite-difference schemes with the discrete transparent boundary conditions (TBCs) to solve it. We first rewrite the discrete TBCs in a…
Solving for the bound state eigenvalues of the Schr\"odinger equation is a tedious iterative process when the conventional shooting or matching method is used. In this work, we bypass the eigenvalue's dependence on the eigenfunction by…
In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…
In this paper we establish the convergence of a numerical scheme based, on the Finite Element Method, for a time-independent problem modelling the deformation of a linearly elastic elliptic membrane shell subjected to remaining confined in…
In this paper, the boundary element method is combined with Chebyshev operational matrix technique to solve two-dimensional multi-order time-fractional partial differential equations; nonlinear and linear in respect to spatial and temporal…
We propose an algorithmic procedure i) to study the ``distance'' between an integrable PDE and any discretization of it, in the small lattice spacing epsilon regime, and, at the same time, ii) to test the (asymptotic) integrability…
In this contribution, we introduce numerical continuation methods and bifurcation theory, techniques which find their roots in the study of dynamical systems, to the problem of tracing the parameter dependence of bound and resonant states…
In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones…