Related papers: Coupled Scheme for Linear and Hamilton-Jacobi Equa…
We numerically investigate, and improve upon, a computational approach originally introduced in [Cottereau, IJNME 2013] which aims at evaluating the effective coefficient of a medium modelled by a highly oscillatory coefficient. This…
The numerical solution of an ordinary differential equation can be interpreted as the exact solution of a nearby modified equation. Investigating the behaviour of numerical solutions by analysing the modified equation is known as backward…
In this paper, a non-uniform time-stepping convex-splitting numerical algorithm for solving the widely used time-fractional Cahn-Hilliard equation is introduced. The proposed numerical scheme employs the $L1^+$ formula for discretizing the…
This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the…
Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…
This contribution is dedicated to the exploration of exponential operator splitting methods for the time integration of evolution equations. It entails the review of previous achievements as well as the depiction of novel results. The…
We present the mathematical study of a computational approach originally introduced by R. Cottereau in [R. Cottereau, IJNME 2013]. The approach aims at evaluating the effective (a.k.a. homogenized) coefficient of a medium with some…
Despite the advances in the development of numerical methods analytical approaches still play the key role on the way towards a deeper understanding of many-particle systems. In this regards, diagonalization schemes for Hamiltonians…
Based on the Scale-Splitting (SCSP) iteration method presented by Hezari et al. in (A new iterative method for solving a class of complex symmetric system linear of equations, Numerical Algorithms 73 (2016) 927-955), we present a new…
In this study, we focus on the modelling of coupled systems of shallow water flows and solute transport with source terms due to variable topography and friction effect. Our aim is to propose efficient and accurate numerical techniques for…
The author presented a stochastic and variational approach to the Lax-Friedrichs finite difference scheme applied to hyperbolic scalar conservation laws and the corresponding Hamilton-Jacobi equations with convex and superlinear…
The present work addresses the Cauchy problem for an abstract nonlinear system of coupled hyperbolic equations associated with the Timoshenko model in a real Hilbert space. Our purpose is to develop and delve into a temporal discretization…
In the first part of this article, we will prove an existence-uniqueness result for generalized solutions of a mixed problem for linear hyperbolic system in the Colombeau algebra. In the second part, we apply this result to a wave…
Variational models with coupling terms are becoming increasingly popular in image analysis. They involve auxiliary variables, such that their energy minimisation splits into multiple fractional steps that can be solved easier and more…
In this paper, some of formulations of Hamilton-Jacobi equations for Hamiltonian system and regular reduced Hamiltonian systems are given. At first, an important lemma is proved, and it is a modification for the corresponding result of…
The aim of this paper is to present a kinetic numerical scheme for the computations of transient pressurised flows in closed water pipes. Firstly, we detail the mathematical model written as a conservative hyperbolic partial differentiel…
We consider linear iterative schemes for the time-discrete equations stemming from a class of nonlinear, doubly-degenerate parabolic equations. More precisely, the diffusion is nonlinear and may vanish or become multivalued for certain…
We propose an explicit partitioned (loosely coupled) scheme for fluid structure interaction (FSI) problems, specifically designed to achieve high computational efficiency in modern engineering simulations. The FSI problem under…
This paper introduces a novel methodology that leverages the Hamilton-Jacobi solution to enhance non-linear model predictive control (MPC) in scenarios affected by navigational uncertainty. Using Hamilton-Jacobi-Theoretic approach, a…
This paper presents a new approach to combine cross-correlation functions. The combination is based on a maximum-likelihood approach and uses a non-linear combination scheme. It can be effective for radial-velocity analysis of multi-order…