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Numerical ordinary differential equation (ODE) solvers are indispensable tools in various engineering domains, enabling the simulation and analysis of dynamic systems. In this work, we utilize 5 different numerical ODE solvers namely:…
Many authors have studied the numerical computation of conformal mappings (numerical conformal mapping), and there are nowadays several efficient numerical schemes. Among them, Amano's method offers a straightforward numerical procedure for…
Accurate path integral Monte Carlo or molecular dynamics calculations of isotope effects have until recently been expensive because of the necessity to reduce three types of errors present in such calculations: statistical errors due to…
We give a number of theoretical and practical methods related to the computation of L-functions, both in the local case (counting points on varieties over finite fields, involving in particular a detailed study of Gauss and Jacobi sums),…
We investigate consistent charged black hole solutions to the Einstein-Maxwell-Dilaton (EMD) equations that are asymptotically AdS. The solutions are gravity duals to phases of a non-conformal plasma at finite temperature and density. For…
Critical heat flux (CHF) marks the transition from nucleate to film boiling, where heat transfer to the working fluid can rapidly deteriorate. Accurate CHF prediction is essential for efficiency, safety, and preventing equipment damage,…
We propose a new iterative scheme to compute the numerical solution to an over-determined boundary value problem for a general quasilinear elliptic PDE. The main idea is to repeatedly solve its linearization by using the quasi-reversibility…
A second-order accurate and robust numerical scheme is developed for the Kapila model to simulate compressible multiphase flows. The scheme is formulated within the finite volume framework with the generalized Riemann problem (GRP) solver…
Estimation of mean shift in a temporally ordered sequence of random variables with a possible existence of change-point is an important problem in many disciplines. In the available literature of more than fifty years the estimation methods…
In mathematical finance, a process of calibrating stochastic volatility (SV) option pricing models to real market data involves a numerical calculation of integrals that depend on several model parameters. This optimization task consists of…
The maximum principle is one of the most important tools in the analysis of geometric partial differential equations. Traditionally, the maximum principle is applied to a scalar function defined on a manifold, but in recent years more…
In many areas of applied mathematics and statistics, it is a fundamental problem to find the best representative of a model by optimizing an objective function. This can be done by determining critical points of the objective function…
We present a new mathematical formulation to estimate the intrinsic parameters of a camera in active or robotic platforms. We show that the focal lengths can be estimated using only one point correspondence that relates images taken before…
Change point analysis has applications in a wide variety of fields. The general problem concerns the inference of a change in distribution for a set of time-ordered observations. Sequential detection is an online version in which new data…
Within the mode-coupling theory (MCT) of the glass transition, we reconsider the numerical schemes to evaluate the MCT functional. Here we propose nonuniform discretizations of the wave number, in contrast to the standard equidistant grid,…
We reconsider the criticality of the Ising model on two-dimensional dynamical triangulations based on the $N \times N$ hermitian two-matrix model with the introduction of a loop-counting parameter and linear terms in the potential. We show…
For a number of tasks, such as 3D reconstruction, robotic interface, autonomous driving, etc., camera calibration is essential. In this study, we present a unique method for predicting intrinsic (principal point offset and focal length) and…
Classical tools of nonlinear dynamics are used to study the highly excited vibrations of small molecules. For effective Hamiltonians with one polyad number (approximate constant of motion), previously developed methods locate new anharmonic…
In the paper, we introduce several accelerate iterative algorithms for solving the multiple-set split common fixed-point problem of quasi-nonexpansive operators in real Hilbert space. Based on primal-dual method, we construct several…
In this paper we propose a novel method to study critical systems numerically by a combined collective-mode algorithm and Renormalization Group on the lattice. This method is an improved version of MCRG in the sense that it has all the…