19 papers · ranked by Valyu relevance
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…
Zhejun Huang, Huiyun Li, Wenfei Li, Jia Liu + 4 more
'Zhiheng Yang' 'Wenqi Fang' 'Soufiene Djahel'] Trajectory tracking is a key technology for precisely controlling autonomous vehicles. In this paper, we propose a trajectory-tracking method based on model predictive control. Instead of using the forward Euler integration method, the backward Euler integration method is…
Davoud Mirzaei
Contents 1 An introduction to ODEs 1 1.1 Modelling with ODEs: a funny example . . . . . . . . . . . . . . . . . . . 4 1.2 Higher order ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 First order system of ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Stability of solutions . .…
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…
Torsten Linß, Natalia Kopteva, Goran Radojev, Martin Ossadnik
A posteriori error estimates in the maximum norm are studied for various time-semidiscretisations applied to a class of linear parabolic equations. We summarise results from the literature and present some new improved error bounds. Crucial ingredients are certain bounds in the L1 norm for the Green's function…
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…
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…
Karoline Horgmo Jæger, James D. Trotter, Xing Cai, Hermenegild Arevalo + 1 more
Computational techniques have significantly advanced our understanding of cardiac electrophysiology, yet they have predominantly concentrated on averaged models that do not represent the intricate dynamics near individual cardiomyocytes. Recently, accurate models representing individual cells have gained popularity…
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
Masho Jima Kabeto, Gemechis File Duressa
Objective The main purpose of this paper is to present an accelerated nonstandard finite difference method for solving the singularly perturbed Burger-Huxley equation in order to produce more accurate solutions. Results The quasilinearization technique is used to linearize the nonlinear term. A nonstandard methodology…
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…
Oday Hazaimah
In this paper we consider a class of second order singular homogeneous differential equations called the Lane-Emden-type with time singularity in the drift coefficient. Lane-Emden equations are singular initial value problems that model phenomena in astrophysics such as stellar structure and are governed by polytropics…
Kevin Zhang, Junhao Zhu, Dehan Kong, Zhaolei Zhang
Recent advances in single-cell sequencing technology have provided opportunities for mathematical modeling of dynamic developmental processes at the single-cell level, such as inferring developmental trajectories. Optimal transport has emerged as a promising theoretical framework for this task by computing pairings…
Lorenzo Micalizzi, Davide Torlo
The deferred correction (DeC) is an iterative procedure, characterized by increasing the accuracy at each iteration, which can be used to design numerical methods for systems of ODEs. The main advantage of such framework is the automatic way of getting arbitrarily high order methods, which can be put in the Runge-Kutta…
Liang Liang, Minliang Liu, John Elefteriades, Wei Sun
Finite-element analysis (FEA) is widely used as a standard tool for stress and deformation analysis of solid structures, including human tissues and organs. For instance, FEA can be applied at a patient-specific level to assist in medical diagnosis and treatment planning, such as risk assessment of thoracic aortic…
Davi Geiger, Michael Werman, Lawrence Horwitz
This paper presents a quantum method to tackle optimization challenges. Departing from the typical applications of quantum theory in particle physics, we demonstrate our approach using the elastica problem as a concrete example. The elastica, a classic variational problem extensively studied by mathematicians, serves…
Authors not listed
Inverse problems, where we seek the values of inputs to a model that lead to a desired set of outputs, are a challenges subset of problems in science and engineering. In this work we demonstrate the use of two generative AI methods to solve inverse problems. We compare this approach to two more conventional approaches…
U. Filobello-Nino, H. Vazquez-Leal, J. Huerta-Chua, D. Mayorga-Cruz + 3 more
'R. Lopez-Leal' 'R.A. Callejas Molina' 'M.A. Sandoval-Hernandez'] The aim of this article is to show a way to extend the usefulness of the Generalized Bernoulli Method (GBM) with the purpose to apply it for the case of variational problems with functionals that depend explicitly of all the variables. Moreover, after…
Rui Zeng, Stefano Sacanna, Saumya Saurabh
Bacterial motility in unconfined liquids is well understood, but many species inhabit crowded, three-dimensional environments where physical constraints shape navigation. Here, we show that the aquatic bacterium Caulobacter crescentus employs backward swimming to overcome confinement, using a force-sensitive mechanism…