Related papers: Stable and accurate numerical methods for generali…
Building upon recent results obtained in [7,8,9], we describe an efficient second order, A-stable scheme for solving the wave equation, based on the method of lines transpose (MOL$^T$), and the resulting semi-discrete (i.e. continuous in…
The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated…
We investigate the finite-time stabilization of a tree-shaped network of strings. Transparent boundary conditions are applied at all the external nodes. At any internal node, in addition to the usual continuity conditions, a modified…
We explore the dynamics of active elements performing persistent random motion with fluctuating active speed and in the presence of translational noise in a $d$-dimensional harmonic trap, modeling active speed generation through an…
Schemes with the second-order approximation in time are considered for numerical solving the Cauchy problem for an evolutionary equation of first order with a self-adjoint operator. The implicit two-level scheme based on the Pad\'{e}…
Towards identifying the number of minimal surfaces sharing the same boundary from the geometry of the boundary, we propose a numerical scheme with high speed and high accuracy. Our numerical scheme is based on the method of fundamental…
Many dynamic pipe flow simulator tools are capable of predicting the onset of hydrodynamic flow instability through detailed simulation. These instabilities provide a natural mechanism for flow regime transition. The quality and reliability…
We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…
We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and is discretized in space using a piecewise-linear Galerkin finite…
We consider a thin and narrow rectangular plate where the two short edges are hinged whereas the two long edges are free. This plate aims to represent the deck of a bridge, either a footbridge or a suspension bridge. We study a nonlocal…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
In this work, we explore various relevant aspects of the Smoothed Particle Hydrodynamics regarding Burger's equation. The stability, precision, and efficiency of the algorithm are investigated in terms of different implementations. In…
We develop a stabilized cut finite element method for the convection problem on a surface based on continuous piecewise linear approximation and gradient jump stabilization terms. The discrete piecewise linear surface cuts through a…
Semi-discrete Galerkin formulations of transient wave equations, either with conforming or discontinuous Galerkin finite element discretizations, typically lead to large systems of ordinary differential equations. When explicit time…
We propose a new family of high-order explicit generalized-$\alpha$ methods for hyperbolic problems with the feature of dissipation control. Our approach delivers $2k,\, \left(k \in \mathbb{N}\right)$ accuracy order in time by solving $k$…
Structure-preserving numerical schemes for a nonlinear parabolic fourth-order equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation…
Approximate analytical solution of two dimensional problem for stationary Navier-Stokes, continuity and Fourier-Kirchhoff equations describing free convective heat transfer from isothermal surface of half infinite vertical plate is…
A thin and narrow rectangular plate having the two short edges hinged and the two long edges free is considered. A nonlinear nonlocal evolution equation describing the deformation of the plate is introduced: well-posedness and existence of…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
We consider the numerical approximations for a phase field model consisting of incompressible Navier--Stokes equations with a generalized Navier boundary condition, and the Cahn-Hilliard equation with a dynamic moving contact line boundary…