The Evolution of Finite Element Approaches in Reaction-Diffusion Modeling

R Sharma, OP Yadav - Archives of Computational Methods in Engineering, 2025‏ - Springer
This paper presents a comprehensive review of finite element methods (FEMs) applied to a
diverse range of reaction-diffusion equations (RDEs). Beginning with a historical overview of …

First-passage problem in random vibrations with radial basis function neural networks

X Wang, J Jiang, L Hong… - … of Vibration and …, 2022‏ - asmedigitalcollection.asme.org
The first-passage time probability plays an important role in the reliability assessment of
dynamic systems in random vibrations. To find the solution of the first-passage time …

A theory of pattern formation for reaction–diffusion systems on temporal networks

RA Van Gorder - Proceedings of the Royal Society A, 2021‏ - royalsocietypublishing.org
Networks have become ubiquitous in the modern scientific literature, with recent work
directed at understanding 'temporal networks'—those networks having structure or topology …

Langevin picture of anomalous diffusion processes in expanding medium

X Wang, Y Chen - Physical Review E, 2023‏ - APS
The expanding medium is very common in many different fields, such as biology and
cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different …

Continuous time random walk in a velocity field: role of domain growth, Galilei-invariant advection-diffusion, and kinetics of particle mixing

F Le Vot, E Abad, R Metzler, SB Yuste - New Journal of Physics, 2020‏ - iopscience.iop.org
We consider the emerging dynamics of a separable continuous time random walk (CTRW)
in the case when the random walker is biased by a velocity field in a uniformly growing …

[HTML][HTML] Time Fractional Fisher–KPP and Fitzhugh–Nagumo Equations

CN Angstmann, BI Henry - Entropy, 2020‏ - mdpi.com
A standard reaction–diffusion equation consists of two additive terms, a diffusion term and a
reaction rate term. The latter term is obtained directly from a reaction rate equation which is …

A class of anomalous diffusion epidemic models based on CTRW and distributed delay

Z Lu, G Ren, Y Chen, X Meng, Y Yu - International Journal of …, 2023‏ - World Scientific
In recent years, the epidemic model with anomalous diffusion has gained popularity in the
literature. However, when introducing anomalous diffusion into epidemic models, they …

Exact sharp-fronted solutions for nonlinear diffusion on evolving domains

ST Johnston, MJ Simpson - Journal of Physics A: Mathematical …, 2023‏ - iopscience.iop.org
Abstract Models of diffusive processes that occur on evolving domains are frequently
employed to describe biological and physical phenomena, such as diffusion within …

Numerical approximation of the first-passage time distribution of time-varying diffusion decision models: A mesh-free approach

AHH Rasanan, NJ Evans, J Rieskamp… - Engineering Analysis with …, 2023‏ - Elsevier
Sequential sampling theory is the dominant theoretical framework for explaining human
decision making behavior. In this theory, the decision process is determined by a stochastic …

[HTML][HTML] Multi-order fractional nonlinear evolution equations system

BH Guswanto, N Istikaanah - Partial Differential Equations in Applied …, 2024‏ - Elsevier
In this paper, the existence and uniqueness of a solution to a multi-order fractional nonlinear
evolution equations system are studied by applying Banach's Fixed Point Theorem and …