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…
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…
Deepjyoti Goswami, Amiya K. Pani
In this paper, a backward Euler method is discussed for the equations of motion arising in the 2D Oldroyd model of viscoelastic fluids of order one with the forcing term independent of time or in L ∞ in time. It is shown that the estimates of the discrete solution in Dirichlet norm is bounded uniformly in time. Optimal…
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…
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…
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…
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…
Yue Wu
In this paper we study the existence and uniqueness of the random periodic solution for a stochastic differential equation with an one-sided Lipschitz condition (also known as monotonicity condition) and the convergence of its numerical approximation via the backward Euler-Maruyama method. The existence of the random…
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
Ahmad Fadly Nurullah Rasedee, Mohammad Hasan Abdul Sathar, Khairil Iskandar Othman, Siti Raihana Hamzah + 2 more
'Khairil Iskandar Othman' 'Siti Raihana Hamzah' 'Norizarina Ishak' 'Naramgari Sandeep'] Differential equations are commonly used to model various types of real life applications. The complexity of these models may often hinder the ability to acquire an analytical solution. To overcome this drawback, numerical methods…
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…
Felice Iavernaro, Francesca Mazzia, Marat S. Mukhametzhanov, Yaroslav D. Sergeyev
'Yaroslav D. Sergeyev'] Multi-derivative one-step methods based upon Euler–Maclaurin integration formulae are considered for the solution of canonical Hamiltonian dynamical systems. Despite the negative result that simplecticity may not be attained by any multi-derivative Runge–Kutta methods, we show that 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.…
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…
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…