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The computation time required by standard finite difference methods with fixed timesteps for solving fractional diffusion equations is usually very large because the number of operations required to find the solution scales as the square of…

Numerical Analysis · Mathematics 2024-06-28 Santos B. Yuste , Joaquin Quintana-Murillo

The aim of this paper is twofold. The first is to study the asymptotics of a parabolically scaled, continuous and space-time stationary in time version of the well-known Funaki-Spohn model in Statistical Physics. After a change of unknowns…

Analysis of PDEs · Mathematics 2020-04-09 Pierre Cardaliaguet , Nicolas Dirr , Panagiotis E. Souganidis

It is well-known that the Fourier-Galerkin spectral method has been a popular approach for the numerical approximation of the deterministic Boltzmann equation with spectral accuracy rigorously proved. In this paper, we will show that such a…

Numerical Analysis · Mathematics 2024-05-08 Liu Liu , Kunlun Qi

In Hamiltonian systems subjected to periodic perturbations the stable and unstable manifolds of the unstable periodic orbits provide the dynamical "skeleton" that drives the mixing process and bounds the chaotic regions of the phase space.…

Plasma Physics · Physics 2016-10-05 David Ciro Taborda , Todd Edwin Evans , Iberê Luiz Caldas

In this article we present our state of the art of fitting helioseismic p-mode spectra. We give a step by step recipe for fitting the spectra: statistics of the spectra both for spatially unresolved and resolved data, the use of Maximum…

Astrophysics · Physics 2009-10-30 T. Appourchaux , L. Gizon , M. C. Rabello-Soares

Regional frequency analysis is an important tool to properly estimate hydrological characteristics at ungauged or partially gauged sites in order to prevent hydrological disasters. The delineation of homogeneous groups of sites is an…

Methodology · Statistics 2016-10-19 Pierre Masselot , Fateh Chebana , Taha B. M. J. Ouarda

For finite-dimensional problems, stochastic approximation methods have long been used to solve stochastic optimization problems. Their application to infinite-dimensional problems is less understood, particularly for nonconvex objectives.…

Optimization and Control · Mathematics 2021-01-14 Caroline Geiersbach , Teresa Scarinci

We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…

Numerical Analysis · Mathematics 2015-11-19 Gil Ariel , Seong Jun Kim , Richard Tsai

In this paper, we employ Tseng's extragradient method with the self-adaptive stepsize to solve variational inequality problems involving non-Lipschitz continuous and quasimonotone operators in real Hilbert spaces. The convergence of the…

Optimization and Control · Mathematics 2025-06-10 Meiying Wang , Hongwei Liu , Jun Yang

In this paper, we develop a new adaptive hyperbolic-cross-space mapped Jacobi (AHMJ) method for solving multidimensional spatiotemporal integrodifferential equations in unbounded domains. By devising adaptive techniques for sparse mapped…

Numerical Analysis · Mathematics 2024-04-12 Yunhong Deng , Sihong Shao , Alex Mogilner , Mingtao Xia

A new algorithm is proposed for solving the three-dimensional scalar inverse problem of acoustic sounding in an inhomogeneous medium. The data for the algorithm are the complex amplitudes of the wave field measured outside the inhomogeneity…

Numerical Analysis · Mathematics 2019-11-26 A. B. Bakushinsky , A. S. Leonov

We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…

Optimization and Control · Mathematics 2025-12-24 Zepeng Wang , Juan Peypouquet

We propose an efficient and easy-to-implement gradient-enhanced least squares Monte Carlo method for computing price and Greeks (i.e., derivatives of the price function) of high-dimensional American options. It employs the sparse Hermite…

Computational Finance · Quantitative Finance 2025-09-01 Jiefei Yang , Guanglian Li

Recently the study of modeling a non-stationary signal as a superposition of amplitude and frequency-modulated Fourier-like oscillatory modes has been a very active research area. The synchrosqueezing transform (SST) is a powerful method…

Numerical Analysis · Mathematics 2018-12-31 Haiyan Cai , Qingtang Jiang , Lin Li , Bruce W. Suter

In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlinear problems with discontinuous diffusion coefficients, such…

Numerical Analysis · Mathematics 2016-08-24 Michael Holst , Ryan Szypowski , Yunrong Zhu

For the accurate representation and reconstruction of band-limited signals on the sphere, an optimal-dimensionality sampling scheme has been recently proposed which requires the optimal number of samples equal to the number of degrees of…

Information Theory · Computer Science 2017-09-11 Wajeeha Nafees , Zubair Khalid , Rodney A. Kennedy , Jason D. McEwen

The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale…

Numerical Analysis · Mathematics 2018-10-22 Doghonay Arjmand , Gunilla Kreiss

A new algorithm for the stable solution of a three-dimensional scalar inverse problem of acoustic sounding of an inhomogeneous medium in a cylindrical region is proposed. The data of the problem is the complex amplitude of the wave field,…

Numerical Analysis · Mathematics 2022-03-30 Anatoly B. Bakushinsky , Alexander S. Leonov

The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…

Plasma Physics · Physics 2024-02-27 Nils W. Schween , Brian Reville

We establish a rate of convergence of the two scale expansion (in the sense of homogenization theory) of the solution to a highly oscillatory elliptic partial differential equation with random coefficients that are a perturbation of…

Analysis of PDEs · Mathematics 2011-10-25 C. Le Bris , F. Legoll , F. Thomines