Related papers: An adaptive homotopy method for computing bifurcat…
We apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied…
Solving partial differential equations (PDEs) using neural networks has become a central focus in scientific machine learning. Training neural networks for singularly perturbed problems is particularly challenging due to certain parameters…
An algorithm is presented here, for discovering Hopf-Bifurcation varieties of polynomial dynamical systems. It is based on the expression of specific polynomials, as sums of products of first degree polynomials, with parametrical…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
Incorporating probabilistic terms in mathematical models is crucial for capturing and quantifying uncertainties in real-world systems, especially when the solution is not unique or exhibits sudden qualitative changes as parameters vary.…
Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis.…
The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…
We comment on the new trend in mathematical physics that consists of obtaining Taylor series for fabricated linear and nonlinear unphysical models by means of homotopy perturbation method (HPM), homotopy analysis method (HAM) and Adomian…
We present a nonlinear equivalent resistance tracking method to optimize the power output for solar arrays. Tracking an equivalent resistance results in nonlinear voltage step sizes in the gradient descent search loop. We introduce a new…
This study presents a theoretical framework for planning and controlling agile bipedal locomotion based on robustly tracking a set of non-periodic apex states. Based on the prismatic inverted pendulum model, we formulate a hybrid…
Conformal inference is a statistical method used to construct prediction sets for point predictors, providing reliable uncertainty quantification with probability guarantees. This method utilizes historical labeled data to estimate the…
PHCpack is a software package for polynomial homotopy continuation, which provides a robust path tracker [Telen, Van Barel, Verschelde, SISC 2020]. This tracker computes the radius of convergence of Newton's method, estimates the distance…
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding…
We consider the extension of the method of Gauss-Newton from complex floating-point arithmetic to the field of truncated power series with complex floating-point coefficients. With linearization we formulate a linear system where the…
In this paper, we propose a novel adaptive finite element method for an elliptic equation with line Dirac delta functions as a source term. We first study the well-posedness and global regularity of the solution in the whole domain. Instead…
We propose a new method of adaptive piecewise approximation based on Sinc points for ordinary differential equations. The adaptive method is a piecewise collocation method which utilizes Poly-Sinc interpolation to reach a preset level of…
In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realized in the semi-discrete finite-volume framework and is based…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
We tackle the boundary control and estimation problems for a class of viscous Hamilton-Jacobi PDEs, considering bilateral actuation and sensing, i.e., at the two boundaries of a 1-D spatial domain. First, we solve the nonlinear trajectory…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…