Related papers: On False Accuracy Verification of UMUSCL Scheme
The construction of finite element approximations in $\mathbf{H}(\mbox{div}, {\Omega})$ usually requires the Piola transformation to map vector polynomials from a master element to vector fields in the elements of a partition of the region…
An important topic of interest in imaging is the construction of protocols that are not diffraction limited. This can be achieved in a variety of ways, including classical superresolution techniques or quantum entanglement-based protocols.…
High-fidelity numerical simulation serves as a cornerstone for exploring magnetization dynamics in micromagnetics. This work introduces a novel third-order temporally accurate and stable numerical scheme for the Landau-Lifshitz-Gilbert…
Confidence curves are used in uncertainty validation to assess how large uncertainties ($u_{E}$) are associated with large errors ($E$). An oracle curve is commonly used as reference to estimate the quality of the tested datasets. The…
A procedure is suggested for testing the resolution and comparing the relative accuracy of numerical schemes for integration of the incompressible Euler equations.
Conventional statistical wisdom established a well-understood relationship between model complexity and prediction error, typically presented as a U-shaped curve reflecting a transition between under- and overfitting regimes. However,…
Exhibiting an explicit Boolean function with a large high-order nonlinearity is an important problem in cryptography, coding theory, and computational complexity. We prove lower bounds on the second-order, third-order, and higher-order…
We consider implementations of high-order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for the Euler equations in cylindrical and spherical coordinate systems with radial dependence only. The main concern of this…
Symmetry analysis of Ramanujan's system of differential equations is performed by representing it as a third-order equation. A new system consisting of a second-order and a first-order equation is derived from Ramanujan's system. The Lie…
High order algorithms have emerged in numerical astrophysics as a promising avenue to reduce truncation error (proportional to a power of the linear resolution $\Delta x$) with only a moderate increase to computational expense. Significant…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…
Although there are many improvements to WENO3-Z that target the achievement of optimal order in the occurrence of the first-order critical point (CP1), they mainly address resolution performance, while the robustness of schemes is of less…
In this paper, a classification of semidiscrete equations of hyperbolic type is carried out. We study the class of equations of the form $$\frac{du_{n+1}}{dx}=f\left(\frac{du_{n}}{dx},u_{n+1},u_{n}\right),$$ here is the unknown function…
We develop a two-dimensional high-order numerical scheme that exactly preserves and captures the moving steady states of the shallow water equations with topography or Manning friction. The high-order accuracy relies on a suitable…
Unsupervised recalibration (URC) is a general way to improve the accuracy of an already trained probabilistic classification or regression model upon encountering new data while deployed in the field. URC does not require any ground truth…
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additive noise in space dimension $d \leq 3$. The full…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
It has now become customary in the field of numerical relativity to couple high order finite difference schemes to mesh refinement algorithms. To this end, different modifications to the standard Berger-Oliger adaptive mesh refinement…
The authors study statistical linear inverse problems in Hilbert spaces. Approximate solutions are sought within a class of linear one-parameter regularization schemes, and the parameter choice is crucial to control the root mean squared…
Fraud detection is a challenging task due to the changing nature of fraud patterns over time and the limited availability of fraud examples to learn such sophisticated patterns. Thus, fraud detection with the aid of smart versions of…