Related papers: Lagrange-mesh calculations and Fourier transform
The augmented Lagrange method is employed to address the optimal control problem involving pointwise state constraints in parabolic equations. The strong convergence of the primal variables and the weak convergence of the dual variables are…
We consider variation of energy of the light-like particle in the pseudo-Riemann space-time, find Lagrangian, canonical momenta and forces. Equations of the critical curve are obtained by the nonzero energy integral variation in accordance…
This paper proposes a very simple perturbative technique to calculate the low-lying eigenvalues and eigenstates of a parity-symmetric quantum-mechanical potential. The technique is to solve the time-independent Schroedinger eigenvalue…
In this paper a spectral-Lagrangian method for the Boltzmann equation for a multi-energy level gas is proposed. Internal energy levels are treated as separate species and inelastic collisions (leading to internal energy excitation and…
We discuss the particle method in quantum mechanics which provides an exact scheme to calculate the time-dependent wavefunction from a single-valued continuum of trajectories where two spacetime points are linked by at most a single orbit.…
We give an algorithm for reversion of formal power series, based on an efficient way to implement the Lagrange inversion formula. Our algorithm requires $O(n^{1/2}(M(n) + MM(n^{1/2})))$ operations where $M(n)$ and $MM(n)$ are the costs of…
Accurate three-body quantal calculations of the system composed of a proton, an antiproton, and an electron are performed in perimetric coordinates with the Lagrange-mesh method, an approximate variational calculation with the simplicity of…
In this work we develop and implement a method for calculation of the Bethe logarithm for many-electron atoms. This quantity is required to evaluate the leading-order quantum electrodynamics correction to the energy and properties of atomic…
This article is devoted to computing the eigenvalue of the Laplace eigenvalue problem by the weak Galerkin (WG) finite element method with emphasis on obtaining lower bounds. The WG method is on the use of weak functions and their weak…
For the quadratic Lagrange interpolation function, an algorithm is proposed to provide explicit and verified bound for the interpolation error constant that appears in the interpolation error estimation. The upper bound for the…
Many-body entanglement is studied within the algebraic approach to quantum physics in systems made of Majorana fermions. In this framework, the notion of separability stems from partitions of the algebra of observables and properties of the…
The Fourier transform method can be applied to obtain electromagnetic knots, which are solutions of Maxwell equations in vacuum with non-trivial topology of the field lines and especial properties. The program followed in this work allows…
Quantum computing has demonstrated the potential to revolutionize our understanding of nuclear, atomic, and molecular structure by obtaining forefront solutions in non-relativistic quantum many-body theory. In this work, we show that…
We have shown that a Lagrangian for a torus surface can yield second order nonlinear differential equations using the Euler-Lagrange formulation. It is seen that these second order nonlinear differential equations can be transformed into…
In this study, we show that the energy eigenvalues and the eigenfunctions of the Schrodinger equation for the power-law and the logarithmic potential can be easily obtained by using variation technique for special type wave functions. The…
The variational iteration method is used to solve nonlinear Volterra integral equations. Two approaches are presented distinguished by the method to compute the Lagrange multiplier.
A novel finite element formulation for gradient-regularized damage models is presented which allows for the robust, efficient, and mesh-independent simulation of damage phenomena in engineering and biological materials. The paper presents a…
We present an efficient method for estimating the eigenvalues of a Hamiltonian $H$ from the expectation values of the evolution operator for various times. For a given quantum state $\rho$, our method outputs a list of eigenvalue estimates…
We propose a novel procedure for handling processes that involve unstable intermediate particles. By using gauge-invariant effective Lagrangians it is possible to perform a gauge-invariant resummation of (arbitrary) self-energy effects. For…
We construct an extended Lagrange FE space to solve the Maxwell equation and its eigenvalue problem in $\mathbb R^d$ $(d=2,3)$, which is the sum of the vectorial $p-$order Lagrange FE space ($p\ge1$) and the gradient of the $p+1-$order…