Related papers: A pseudo-spectral Strang splitting method for line…
In this paper, we offer a comparison in terms of computational efficiency between two techniques to avoid order reduction when using Strang method to integrate nonlinear initial boundary value problems with time-dependent boundary…
We propose a fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries on a Cartesian grid. We employ the ARMS technique to give an explicit and accurate representation of moving…
In this paper, we consider the initial boundary value problem of the two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations. An alternating direction implicit (ADI) spectral method is developed based on…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
Split form schemes for Euler and Navier-Stokes equations are useful for computation of turbulent flows due to their better robustness. This is because they satisfy additional conservation properties of the governing equations like kinetic…
Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…
We analyze the convergence of the exponential Lie and exponential Strang splitting applied to inhomogeneous second-order parabolic equations with Dirichlet boundary conditions. A recent result on the smoothing properties of these methods…
Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…
Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the Semi-Lagrangian approach to diffusion and advection--diffusion problems have been proposed recently. These…
We focus here on a class of fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. We design a novel second-order fully discrete mixed finite element method to…
This paper presents a spatial two-grid (STG) compact difference scheme for a two-dimensional (2D) nonlinear diffusion-wave equation with variable exponent, which describes, e.g., the propagation of mechanical diffusive waves in viscoelastic…
High-dimensional transport equations frequently occur in science and engineering. Computing their numerical solution, however, is challenging due to its high dimensionality. In this work we develop an algorithm to efficiently solve the…
In this paper, an alternating direction implicit (ADI) difference scheme for two-dimensional time-fractional wave equation of distributed-order with a nonlinear source term is presented. The unique solvability of the difference solution is…
Purely dispersive partial differential equations as the Korteweg-de Vries equation, the nonlinear Schr\"odinger equation and higher dimensional generalizations thereof can have solutions which develop a zone of rapid modulated oscillations…
Tracer diffusion and hydrodynamic dispersion in two-dimensional fractures with self-affine roughness is studied by analytic and numerical methods. Numerical simulations were performed via the lattice-Boltzmann approach, using a new boundary…
In this paper we want to propose practical numerical methods to solve a class of initial-boundary problem of time-space fractional convection-diffusion equations (TSFCDEs). To start with, an implicit difference method based on two-sided…
In this paper we present an efficient discretization method for the solution of the unsteady incompressible Navier-Stokes equations based on a high order (Hybrid) Discontinuous Galerkin formulation. The crucial component for the efficiency…
A reaction-diffusion problem with a Caputo time derivative is considered. An integral discretization scheme on a graded mesh along with a decomposition of the exact solution is proposed. The truncation error estimate of the discretization…
The widespread adoption of distributed learning to train a global model from local data has been hindered by the challenge posed by stragglers. Recent attempts to mitigate this issue through gradient coding have proved difficult due to the…
In this article, we have developed a higher order compact numerical method for variable coefficient parabolic problems with mixed derivatives. The finite difference scheme, presented here for two-dimensional domains, is based on fourth…