Related papers: Analytical Approximate Solution of a Coupled Two F…
The perturbation method is an approximation scheme with a solvable leading order. The standard way is to choose a non-interacting sector for the leading order. The adaptive perturbation method improves the solvable part by using all…
By the introduction of a generalized Evans function defined by an appropriate 2-modified Fredholm determinant, we give a simple proof of convergence in location and multiplicity of Hill's method for numerical approximation of spectra of…
We consider the numerical integration of the matrix Hill's equation. Parametric resonances can appear and this property is of great interest in many different physical applications. Usually, the Hill's equations originate from a Hamiltonian…
The method for analytic evaluation of four-particle integrals, proposed by Fromm and Hill, is generalized to include complex exponential parameters. An original procedure of numerical branch tracking for multiple valued functions is…
This paper reviews recent results on hybrid inverse problems, which are also called coupled-physics inverse problems of multi-wave inverse problems. Inverse problems tend to be most useful in, e.g., medical and geophysical imaging, when…
We propose a practical method to solve the random-phase approximation (RPA) in the self-consistent Hartree-Fock (HF) and density-functional theory. The method is based on numerical evaluation of the residual interactions utilizing finite…
We present a method to obtain arbitrarily accurate solutions for conservative classical oscillators. The method that we propose here works both for small and large nonlinearities and provides simple analytical approximations. A comparison…
The auxiliary field method is a powerful technique to obtain approximate closed-form energy formulas for eigenequations in quantum mechanics. Very good results can be obtained for Schr\"odinger and semirelativistic Hamiltonians with various…
We study the exact Bethe Ansatz solution of the p+ip Hamiltonian in a form whereby quantum numbers of states refer to hole-pairs, rather than particle-pairs used in previous studies. We find an asymmetry between these approaches. For the…
We derive the approximate solution for the pairing Hamiltonian in the Berggren ensemble of single particle states including bound, resonance and non-resonant scattering states. We show that this solution is reliable in the limit of a weak…
We analyze a system of reacting elements harmonically coupled to nearest neighbors in the continuum limit. An analytic solution is found for traveling waves. The procedure is used to find oscillatory as well as solitary waves. A comparison…
We apply the convergent close-coupling (CCC) formalism to the problem of two-photon double ionization of helium. The electron-photon interaction is treated perturbatively whereas the electron-electron interaction is included in full. The…
In this paper, we consider the Fourier spectral method for numerically solving the 2D convective Cahn-Hilliard equation. The semi-discrete and fully discrete schemes are established. Moreover, the existence, uniqueness and the optimal error…
Boundary element methods for the Helmholtz equation lead to large dense matrices that can only be handled if efficient compression techniques are used. Directional compression techniques can reach good compression rates even for…
Attosecond chronoscopy typically utilises interfering two-photon transitions to access the phase information. Simulating these two-photon transitions is challenging due to the continuum-continuum transition term. The hydrogenic…
We show that the Lindstedt-Poincare perturbation theory is always a reliable technique in the region of small coupling constant. The harmonic balance result, on the other hand, if expanded in the perturbation parameter may lead to incorrect…
We found that the two-dimensional Schr\"odinger equation for 3 electrons in an homogeneous magnetic field (perpendicular to the plane) and a parabolic scalar confinement potential (frequency $\omega_0$) has exact analytical solutions in the…
We construct approximate analytical solutions to the constraint equations of general relativity for binary black holes of arbitrary mass ratio in quasicircular orbit. We adopt the puncture method to solve the constraint equations in the…
The simplest, algebraic quantum-electrodynamical corrections, due to the double-negative energy subspace and instantaneous interactions, are computed to the no-pair energy of two-spin-1/2-fermion systems. Numerical results are reported for…
Numerical studies are presented to assess error estimates for a separable (Hartree) approximation for dynamically evolving composite quantum systems which exhibit distinct scales defined by their mass and frequency ratios. The relevant…