Related papers: A stability preserved time-integration method for …
This paper presents a new method to approximate the time-dependent convection-diffusion equations using conforming finite element methods, ensuring that the discrete solution respects the physical bounds imposed by the differential…
The choice of numerical integrator in approximating solutions to dynamic partial differential equations depends on the smallest time-scale of the problem at hand. Large-scale deformations in elastic solids contain both shear waves and bulk…
The lattice Boltzmann method (LBM) for the variable-coefficient forced Burgers equation (vc-FBE) is studied by choosing the equilibrium distribution and compensatory functions properly. In our model, the vc-FBE is correctly recovered via…
Modeling the time-dependent evolution of electron density is essential for understanding quantum mechanical behaviors of condensed matter and enabling predictive simulations in spectroscopy, photochemistry, and ultrafast science. Yet, while…
We study a class of 1+1 quadratically nonlinear water wave equations that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still preserves…
Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…
This paper deals with a new algorithm called modified trigonometric cubic B-spline differential quadrature method for numerical computation of the time dependent partial differential equations. Specially the numerical computation of the…
In this paper, a multiple-distribution-function finite-difference lattice Boltzmann method (MDF-FDLBM) is proposed for the convection-diffusion system based incompressible Navier-Stokes equations (NSEs). By Chapman Enskog analysis, the…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. We interchangeably use particle and grid representations of transported quantities to balance efficiency and accuracy. A novel…
We study the discretization, convergence, and numerical implementation of recent reformulations of the quadratic porous medium equation (multidimensional and anisotropic) and Burgers' equation (one-dimensional, with optional viscosity), as…
In this work, we use the spectral Galerkin method to prove the existence of a pathwise unique mild solution of a fractional stochastic partial differential equation of Burgers type in a H\"older space. We get the temporal regularity and…
The inviscid Burgers equation is one of the simplest nonlinear hyperbolic conservation law which provides a variety examples for many topics in nonlinear partial differential equations such as wave propagation, shocks and perturbation, and…
Efficient time integration methods based on operator splitting are introduced for the Westervelt equation, a nonlinear damped wave equation that arises in nonlinear acoustics as mathematical model for the propagation of sound waves in high…
We develop a mathematical framework to analyze electrochemical impedance spectra in terms of a distribution of diffusion times (DDT) for a parallel array of random finite-length Warburg (diffusion) or Gerischer (reaction-diffusion) circuit…
We carry out enhanced symmetry analysis of a two-dimensional Burgers system. The complete point symmetry group of this system is found using an enhanced version of the algebraic method. Lie reductions of the Burgers system are…
We address a new numerical scheme based on a class of machine learning methods, the so-called Extreme Learning Machines with both sigmoidal and radial-basis functions, for the computation of steady-state solutions and the construction of…
In this paper, we propose high order numerical methods to solve a 2D advection diffusion equation, in the highly oscillatory regime. We use an integrator strategy that allows the construction of arbitrary high-order schemes {leading} to an…
A very simple and efficient local variational iteration method for solving problems of nonlinear science is proposed in this paper. The analytical iteration formula of this method is derived first using a general form of first order…
We consider an integro-differential equation model for traffic flow which is an extension of the Burgers equation model. To discuss the model, we first examine general settings for integrable integro-differential equations and find that…