Related papers: Matrix-oriented discretization methods for reactio…
The propagation of electromagnetic waves in general media is modeled by the time-dependent Maxwell's partial differential equations (PDEs), coupled with constitutive laws that describe the response of the media. In this work, we focus on…
Variational formulations of time-dependent PDEs in space and time yield $(d+1)$-dimensional problems to be solved numerically. This increases the number of unknowns as well as the storage amount. On the other hand, this approach enables…
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would…
In this article, we propose novel boundary treatment algorithms to avoid order reduction when implicit-explicit Runge-Kutta time discretization is used for solving convection-diffusion-reaction problems with time-dependent Di\-richlet…
In the present work, we investigate a model of the invasion of healthy tissue by cancer cells which is described by a system of nonlinear PDEs consisting of a cross-diffusion-reaction equation and two additional nonlinear ordinary…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
We develop a convergent reaction-drift-diffusion master equation (CRDDME) to facilitate the study of reaction processes in which spatial transport is influenced by drift due to one-body potential fields within general domain geometries. The…
We construct four variants of space-time finite element discretizations based on linear tensor-product and simplex-type finite elements. The resulting discretizations are continuous in space, and continuous or discontinuous in time. In a…
We provide a preliminary comparison of the dispersion properties, specifically the time-amplification factor, the scaled group velocity and the error in the phase speed of four spatiotemporal discretization schemes utilized for solving the…
Biological, physical, medical, and numerical applications involving membrane problems on different scales are numerous. We propose an extension of the standard Turing theory to the case of two domains separated by a permeable membrane. To…
We present a unified framework for solving partial differential equations (PDEs) using video-inpainting diffusion transformer models. Unlike existing methods that devise specialized strategies for either forward or inverse problems under…
Stochastic differential equations (SDEs) are a fundamental tool for modelling dynamic processes, including gene regulatory networks (GRNs), contaminant transport, financial markets, and image generation. However, learning the underlying SDE…
Traditionally, systems governed by linear Partial Differential Equations (PDEs) are spatially discretized to exploit their algebraic structure and reduce the computational effort for controlling them. Due to beneficial insights of the PDEs,…
A general system of several ordinary differential equations coupled with a reaction-diffusion equation in a bounded domain with zero-flux boundary condition is studied in the context of pattern formation. These initial-boundary value…
Solving partial differential equations (PDEs) on fine spatio-temporal scales for high-fidelity solutions is critical for numerous scientific breakthroughs. Yet, this process can be prohibitively expensive, owing to the inherent complexities…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
The Time Domain-Electric Field Integral Equation (TD-EFIE) and its differentiated version are widely used to simulate the transient scattering of a time dependent electromagnetic field by a Perfect Electrical Conductor (PEC). The time…
By discretising space into compartments and letting system dynamics be governed by the reaction-diffusion master equation, it is possible to derive and simulate a stochastic model of reaction and diffusion on an arbitrary domain. However,…
Generative diffusion models have achieved remarkable success in producing high-quality images. However, these models typically operate in continuous intensity spaces, diffusing independently across pixels and color channels. As a result,…
A fourth-order exponential time differencing (ETD) Runge-Kutta scheme with dimensional splitting is developed to solve multidimensional non-linear systems of reaction-diffusion equations (RDE). By approximating the matrix exponential in the…