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Stochastic space-time fractional diffusion equations often appear in the modeling of the heat propagation in non-homogeneous medium. In this paper, we firstly investigate the Mittag--Leffler Euler integrator of a class of stochastic…

Numerical Analysis · Mathematics 2023-08-15 Xinjie Dai , Jialin Hong , Derui Sheng

We present results on tagged particle diffusion in a meso-scale lattice model for sheared amorphous material in athermal quasi-static conditions. We find a short time diffusive regime and a long time diffusive regime whose diffusion…

Soft Condensed Matter · Physics 2018-10-10 Botond Tyukodi , Craig E Maloney , Damien Vandembroucq

We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…

Functional Analysis · Mathematics 2024-06-17 Lyndsay Kerr , Wilson Lamb , Matthias Langer

This paper contributes with a new formal method of spatial discretization of a class of nonlinear distributed parameter systems that allow a port-Hamiltonian representation over a one dimensional manifold. A specific finite dimensional…

Numerical Analysis · Mathematics 2021-04-23 B. C. van Huijgevoort , S. Weiland , H. J. Zwart

Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…

Numerical Analysis · Mathematics 2020-05-29 Lehel Banjai , Christian Lubich , Joerg Nick

This paper introduces improved numerical techniques for addressing numerical boundary and interface coupling conditions in the context of diffusion equations in cellular biophysics or heat conduction problems in fluid-structure…

Numerical Analysis · Mathematics 2025-02-27 Taj Munir , Nagaiah Chamakuri , Gerald Warnecke

In this work, we present a conditionally stable finite-difference scheme that consistently approximates the solution of a general class of (3+1)-dimensional nonlinear equations that generalizes in various ways the quantitative model…

Numerical Analysis · Mathematics 2011-12-26 J. E. Macías-Díaz , A. Puri

A class of second order approximations, called the weighted and shifted Gr\"{u}nwald difference operators, are proposed for Riemann-Liouville fractional derivatives, with their effective applications to numerically solving space fractional…

Numerical Analysis · Mathematics 2015-04-27 WenYi Tian , Han Zhou , Weihua Deng

We study linear stability of exponential periodic solutions of a system of singular amplitude equations associated with convective Turing bifurcation in the presence of conservation laws, as arises in modern biomorphology models, binary…

Analysis of PDEs · Mathematics 2025-07-01 Aric Wheeler , Kevin Zumbrun

Plane-wave Trefftz methods (PWB) for the Helmholtz equation offer significant advantages over standard discretization approaches whose implementation employs more general polynomial basis functions. A disadvantage of these methods is the…

Numerical Analysis · Mathematics 2025-09-19 Joseph Coyle , Nilima Nigam

The functional distributions of particle trajectories have wide applications, including the occupation time in half-space, the first passage time, and the maximal displacement, etc. The models discussed in this paper are for characterizing…

Numerical Analysis · Mathematics 2017-07-27 Zhijiang Zhang , Weihua Deng

Although diffusion models now occupy a central place in generative modeling, introductory treatments commonly assume Euclidean data and seldom clarify their connection to discrete-state analogues. This article is a self-contained primer on…

Machine Learning · Statistics 2025-12-05 Vincent Pauline , Tobias Höppe , Kirill Neklyudov , Alexander Tong , Stefan Bauer , Andrea Dittadi

In this paper, we are interested in an efficient numerical method for the mixed-dimensional approach to modeling single-phase flow in fractured porous media. The model introduces fractures and their intersections as lower-dimensional…

Numerical Analysis · Mathematics 2019-06-03 Ana Budiša , Xiaozhe Hu

This is the first in a series of papers on implementing a discontinuous Galerkin method as a MATLAB / GNU Octave toolbox. The main goal is the development of techniques that deliver optimized computational performance combined with a…

Numerical Analysis · Mathematics 2018-06-12 Florian Frank , Balthasar Reuter , Vadym Aizinger , Peter Knabner

Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…

Numerical Analysis · Mathematics 2010-02-16 Liudmila Rozanova

This work focuses on the derivation and the analysis of a novel, strongly-coupled partitioned method for fluid-structure interaction problems. The flow is assumed to be viscous and incompressible, and the structure is modeled using linear…

Numerical Analysis · Mathematics 2022-11-09 Martina Bukac , Anyastassia Seboldt , Catalin Trenchea

In the present paper, we are concerned with the study of matrix-sequences arising from the discretization of PDEs and FDEs on domains $\Omega \subset \mathbb{R}^d$ with finite measure. When $\Omega$ is either a hypercube or a bounded…

Numerical Analysis · Mathematics 2026-03-02 Andrea Adriani , Alec Jacopo Almo Schiavoni-Piazza

We consider difference schemes for the time-fractional diffusion equation with variable coefficients and nonlocal boundary conditions containing real parameters $\alpha$, $\beta$ and $\gamma$. By the method of energy inequalities, for the…

Numerical Analysis · Mathematics 2014-05-02 A. A. Alikhanov

We present parameter-robust preconditioners for linear systems that arise after applying static condensation to a hybridizable discontinuous Galerkin (HDG) discretization of the time-dependent Stokes problem. Building upon the theoretical…

Numerical Analysis · Mathematics 2026-04-09 Esteban Henríquez , Jeonghun J. Lee , Sander Rhebergen

This paper is concerned with the design, analysis and implementation of preconditioning concepts for spectral Discontinuous Galerkin discretizations of elliptic boundary value problems. While presently known techniques realize a growth of…

Numerical Analysis · Mathematics 2014-05-14 Kolja Brix , Martin Campos Pinto , Claudio Canuto , Wolfgang Dahmen