Related papers: Accurate Spectral Collocation Computation of High …
The present contribution concerns the computation of energy eigenvalues of a perturbed anharmonic coulombic potential with irregular singularities using a combination of the Sinc collocation method and the double exponential transformation.…
We present algorithms for computing strongly singular and near-singular surface integrals over curved triangular patches, based on singularity subtraction, the continuation approach, and transplanted Gauss quadrature. We demonstrate the…
We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our…
We show that a pseudospectral representation of the wavefunction using multiple spatial domains of variable size yields a highly accurate, yet efficient method to solve the time-dependent Schr\"odinger equation. The overall spatial domain…
It is generally known that in order to solve the split equality fixed-point problem (SEFPP), it is necessary to compute the norm of bounded and linear operators, which is a challenging task in real life, to address this issue, we studied…
We present a novel approach to accelerate iterative methods to solve nonlinear Schr\"odinger eigenvalue problems using neural networks. Nonlinear eigenvector problems are fundamental in quantum mechanics and other fields, yet conventional…
Three pseudospectral algorithms are described (Euler, leapfrog and trapez) for solving numerically the time dependent nonlinear Schroedinger equation in one, two or three dimensions. Numerical stability regions in the parameter space are…
Due to the good performance of neural networks in high-dimensional and nonlinear problems, machine learning is replacing traditional methods and becoming a better approach for eigenvalue and wave function solutions of multi-dimensional…
A symmetric characteristic singular integral equation with two fixed singularities at the endpoints in the class of functions bounded at the ends is analyzed. It reduces to a vector Hilbert problem for a half-disc and then to a vector…
Singular source terms expressed as weighted summations of Dirac-delta functions are regularized through approximation theory with convolution operators. We consider the numerical solution of scalar and one-dimensional hyperbolic…
The normal mode model is one of the most popular approaches for solving underwater sound propagation problems. Among other methods, the finite difference method is widely used in classic normal mode programs. In many recent studies, the…
Singularly perturbed boundary value problems pose a significant challenge for their numerical approximations because of the presence of sharp boundary layers. These sharp boundary layers are responsible for the stiffness of solutions, which…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
With the regular decomposition technique, we decompose the space $\mathbf{H}_0^s(\mathbf{curl}; \Omega)$ into the sum of a vector potential space and the gradient of a scalar space, both possessing higher regularity. Based on this new high…
Boundary integral methods are highly suited for problems with complicated geometries, but require special quadrature methods to accurately compute the singular and nearly singular layer potentials that appear in them. This paper presents a…
This paper investigates the convergence properties of spectral algorithms -- a class of regularization methods originating from inverse problems -- under covariate shift. In this setting, the marginal distributions of inputs differ between…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
We develop a practical approach to semidefinite programming (SDP) that includes the von Neumann entropy, or an appropriate variant, as a regularization term. In particular we solve the dual of the regularized program, demonstrating how a…
This work concerns the distance in 2-norm from a matrix polynomial to a nearest polynomial with a specified number of its eigenvalues at specified locations in the complex plane. Perturbations are allowed only on the constant coefficient…
This paper offers a review of numerical methods for computation of the eigenvalues of Hermitian matrices and the singular values of general and some classes of structured matrices. The focus is on the main principles behind the methods that…