20 papers · ranked by Valyu relevance
Janosch Rieger
Two semi-implicit Euler schemes for differential inclusions are proposed and analyzed in depth. An error analysis shows that both semiimplicit schemes inherit favorable stability properties from the differential inclusion. Their performance is considerably better than that of the implicit Euler scheme, because instead…
K. R. Arun, S. Samantaray
We consider two distinguished asymptotic limits of the Euler equations in a gravitational field, namely the incompressible and Boussinesq limits. Both these limits can be obtained as singular limits of the Euler equations under appropriate scaling of the Mach and Froude numbers. We propose and analyse an asymptotic…
Sebastiano Boscarino, Giovanni Russo, Leonardo Scandurra
This paper presents an asymptotic preserving (AP) all Mach number finite volume shock capturing method for the numerical solution of compressible Euler equations of gas dynamics. Both isentropic and full Euler equations are considered. The equations are discretized on a staggered grid. This simplifies flux computation…
Kaiwen Shi, Haiyan Su, Xinlong Feng, Eun-jin Kim
In this article, we mainly consider a first order penalty finite element method (PFEM) for the 2D/3D unsteady incompressible magnetohydrodynamic (MHD) equations. The penalty method applies a penalty term to relax the constraint “ $\nabla\cdotu=0$”, which allows us to transform the saddle point problem into two smaller…
Saurav Samantaray
Schemes for Low Mach Number Isentropic Euler Equations Authors: ['Saurav Samantaray'] - Abstract. We consider the compressible Euler equations of gas dynamics with isentropic equation of state. Standard numerical schemes for the Euler equations suffer from stability and accuracy issues in the low Mach regime. These…
Giacomo Albi, Lorenzo Pareschi
We consider the construction of semi-implicit linear multistep methods which can be applied to time dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As shown in [9] for Runge-Kutta methods, these semi-implicit techniques give a great…
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…
Authors not listed
The aim of this work is to apply a semi-implicit (SI) strategy within a Rosenbrocktype and IMEX linear multistep (LM) framework to a sequence of 1D time-dependent partial differential equations (PDEs) with high order spatial derivatives. This strategy provides great flexibility to treat these equations, and allows the…
Peter Frolkovič, Karol Mikula
A new parametric class of semi-implicit numerical schemes for a level set advection equation on Cartesian grids is derived and analyzed. An accuracy and a stability study is provided for a linear advection equation with a variable velocity using partial Lax-Wendroff procedure and numerical von Neumann stability…
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…
R. Abgrall
We show how to combine in a natural way (i.e., without any test nor switch) the conservative and non-conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different classes of schemes: the residual distribution one (Abgrall in Commun Appl Math Comput 2(3): 341-368…
Nikolai D. Lipscomb, Daniel X. Guo
Semi-Lagrangian methods are numerical methods designed to find approximate solutions to particular time-dependent partial differential equations (PDEs) that describe the advection process. We propose semi-Lagrangian one-step methods for numerically solving initial value problems for two general systems of partial…
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…
Ling Zhang
The main purpose of this paper is to investigate the strong convergence and exponential stability in mean square of the exponential Euler method to semi-linear stochastic delay differential equations (SLSDDEs). It is proved that the exponential Euler approximation solution converges to the analytic solution with the…
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…
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…
Joyce Reimer, Sebastián A. Domínguez-Rivera, Joakim Sundnes, Raymond J. Spiteri
The refractory period of cardiac tissue can be quantitatively described using strength-interval (SI) curves. The information captured in SI curves is pertinent to the design of anti-arrhythmic devices including pacemakers and implantable cardioverter defibrillators. As computational cardiac modelling becomes more…
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…
Lukas F. Lang, Nilankur Dutta, Elena Scarpa, Bénédicte Sanson + 2 more
We propose a variational method for joint motion estimation and source identification in one-dimensional image sequences. The problem is motivated by fluorescence microscopy data of laser nanoablations of cell membranes in live Drosophila embryos, which can be conveniently—and without loss of significant…
U. Filobello-Nino, H. Vazquez-Leal, M. M. Rashidi, H. M. Sedighi + 10 more
'A. Perez-Sesma' 'M. Sandoval-Hernandez' 'A. Sarmiento-Reyes' 'A. D. Contreras-Hernandez' 'D. Pereyra-Diaz' 'C. Hoyos-Reyes' 'V. M. Jimenez-Fernandez' 'J. Huerta-Chua' 'F. Castro-Gonzalez' 'J. R. Laguna-Camacho'] This article proposes the application of Laplace Transform-Homotopy Perturbation Method and some of its…