Related papers: An accurate numerical method for systems of differ…
The use of implicit time-stepping schemes for the numerical approximation of solutions to stiff nonlinear time-evolution equations brings well-known advantages including, typically, better stability behaviour and corresponding support of…
We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed. The numerical scheme is constructed based on the variational multiscale formulation and the…
We present a modification of Newton's method to restore quadratic convergence for isolated singular solutions of polynomial systems. Our method is symbolic-numeric: we produce a new polynomial system which has the original multiple solution…
A procedure to numerically integrate non-autonomous linear delay differential equations is presented. It is based on the use of an spectral discretization of the delayed part to transform the original problem into a matrix linear ordinary…
In this work, we study a system of coupled Cahn-Hilliard equations describing the phase separation of a copolymer and a homopolymer blend. The numerical methods we propose are based on suitable combinations of existing schemes for the…
The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high…
We describe an implicit procedure for solving linear equation systems resulting from the discretization of the three dimensional (seven variables) linear Fokker-Planck equation. The discretization of the Fokker-Planck equation is performed…
We consider a non-isothermal compositional gas liquid model for the simulation of well operations in geothermal processes. The model accounts for phase transitions assumed to be at thermodynamical equilibrium and is based on an…
We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. In comparison with recent advances in this vein, the…
This paper is concerned with numerical approximation of some two-dimensional Keller-Segel chemotaxis models, especially those generating pattern formations. The numerical resolution of such nonlinear parabolic-parabolic or…
Time-implicit schemes are attractive since they allow numerical time steps that are much larger than those permitted by the Courant-Friedrich-Lewy criterion characterizing time-explicit methods. This advantage comes, however, with a cost:…
In this paper, a fractional step lattice Boltzmann method is proposed to model two-phase flows with large density differences by solving Cahn-Hilliard phase-field equation and the incompressible Navier-Stokes equations.In order to maintain…
Nonlinear elliptic problems arise in many fields, including plasma physics, astrophysics, and optimal transport. In this article, we propose a novel operator-splitting/finite element method for solving such problems. We begin by introducing…
A methodology is presented for the numerical solution of nonlinear elliptic systems in unbounded domains, consisting of three elements. First, the problem is posed on a finite domain by means of a proper nonlinear change of variables. The…
In this paper, we propose an inexact Newton-like conditional gradient method for solving constrained systems of nonlinear equations. The local convergence of the new method as well as results on its rate are established by using a general…
We study a numerical approximation for a nonlinear variable-order fractional differential equation via an integral equation method. Due to the lack of the monotonicity of the discretization coefficients of the variable-order fractional…
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…
We describe a new method of calculation of generic multi-loop master integrals based on the numerical solution of systems of difference equations in one variable. We show algorithms for the construction of the systems using…
We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient solution process. Purely numerical algorithms typically have…
In reservoir simulation, solution of the coupled systems of nonlinear algebraic equations that are associated with fully-implicit (backward Euler) discretization is challenging. Having a robust and efficient nonlinear solver is necessary in…