18 papers · ranked by Valyu relevance
Yu Zhang, Longsuo Li
In this paper, we concern stability of numerical methods applied to stochastic delay integro-differential equations. For linear stochastic delay integro-differential equations, it is shown that the mean-square stability is derived by the split-step backward Euler method without any restriction on step-size, while the…
Sonja Mathias, Adrien Coulier, Andreas Hellander
Background Cell-based models are becoming increasingly popular for applications in developmental biology. However, the impact of numerical choices on the accuracy and efficiency of the simulation of these models is rarely meticulously tested. Without concrete studies to differentiate between solid model conclusions and…
Sergio Blanes, Fernando Casas, Ander Murua
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class of integrators are composition methods, in which one or several low-order schemes…
Letizia Angeli, Dan Crisan, Michela Ottobre
| 1. Introduction | | 1 | | --- | --- | --- | | 1.1. | Main results and relation to literature | 3 | | 2. | A general result for uniform weak Convergence | 6 | | 2.1. | Sufficient conditions for Strong Exponential Stability (condition (7a)) | 10 | | 3. | Euler-Maruyama Schemes for SDEs with Lipschitz coefficients | 12…
Boris Shabash, Kay C. Wiese
Background RNA visualization software tools have traditionally presented a static visualization of RNA molecules with limited ability for users to interact with the resulting image once it is complete. Only a few tools allowed for dynamic structures. One such tool is jViz.RNA. Currently, jViz.RNA employs a unique…
Sonja Mathias, Adrien Coulier, Andreas Hellander
Cell-based models are becoming increasingly popular for applications in developmental biology. However, the impact of numerical choices on the accuracy and efficiency of the simulation of these models is rarely meticulously tested. We present CBMOS, a Python framework for the simulation of the center-based or…
James M. Osborne
In recent years, multi–cellular models, where cells are represented as individual interacting entities, are becoming ever popular. This has led to a proliferation of novel methods and simulation tools. The first aim of this paper is to review the numerical methods utilised by multi–cellular modelling tools and to…
Shingyu Leung
We propose implicit integrators for solving stiff differential equations on unit spheres. Our approach extends the standard backward Euler and Crank-Nicolson methods in Cartesian space by incorporating the geometric constraint inherent to the unit sphere without additional projection steps to enforce the unit length…
Kai Diethelm
Fractional order models have proven to be a very useful tool for the modeling of the mechanical behaviour of viscoelastic materials. Traditional numerical solution methods exhibit various undesired properties due to the non-locality of the fractional differential operators, in particular regarding the high…
M.A. Botchev, В. Т. Жуков
—In this paper a variant of nonlinear exponential Euler scheme is proposed for solving nonlinear heat conduction problems. The method is based on nonlinear iterations where at each iteration a linear initial-value problem has to be solved. We compare this method to the backward Euler method combined with nonlinear…
Riccardo Russo, Michele Ducceschi, Stefan Bilbao
This work is concerned with the Scalar Auxiliary Variable (SAV) method applied to geometrically nonlinear string models, focusing on the analysis of numerical convergence across various model formulations. An ODE system with a potential akin to that of the geometrically exact string is first analysed, providing both…
Roger Käppeli
We review well-balanced methods for the faithful approximation of solutions of systems of hyperbolic balance laws that are of interest to computational astrophysics. Well-balanced methods are specialized numerical techniques that guarantee the accurate resolution of non-trivial steady-state solutions, that balance laws…
Uwe Naumann
with differentiable right-hand side G : R × Rn → Rn from an initial state x = x(0) ∈ Rn to a target time t ∈ R as x(t) = E(t, m, x) using an equidistant discretization of the time interval [0, t] yielding m > 0 time steps. We present a method for efficiently computing the product of its inverse Jacobian
Helia Mojtabavi, Atra Ajdari, Sebastian Rueda-Parra, Darren E. Gemoets + 2 more
Human locomotion is a highly adaptive motor skill that adjusts to new environmental demands through learning. Split-belt treadmill paradigms have advanced our understanding of gait adaptation. Most studies have examined gait when the belts move at different speeds in the same direction. We are studying muscle…
Sam Motsoka Rametse, Sheldon Herbst
Accurate and stable numerical simulation of epidemic dynamics is essential for translating mathematical models into reliable computational tools for public health. The Susceptible–Infectious–Recovered (SIR) model remains a cornerstone of mathematical epidemiology, yet the robustness of its numerical treatment strongly…
Peter E. Hydon
The problem of inverting the total divergence operator is central to finding components of a given conservation law. This might not be taxing for a low-order conservation law of a scalar partial differential equation, but integrable systems have conservation laws of arbitrarily high order that must be found with the…
Giuseppe de Alteriis, Enrico Cataldo, Alberto Mazzoni, Calogero Maria Oddo
The Izhikevich artificial spiking neuron model is among the most employed models in neuromorphic engineering and computational neuroscience, due to the affordable computational effort to discretize it and its biological plausibility. It has been adopted also for applications with limited computational resources in…
Alfred S Carasso
Identifying sources of ground water pollution, and deblurring nanoscale imagery as well as astronomical galaxy images, are two important applications involving numerical computation of parabolic equations backward in time. Surprisingly, very little is known about backward continuation in nonlinear parabolic equations.…