Related papers: A splitting approach for freezing waves
We investigate a local modification of a variable-order fractional wave equation, which describes the propagation of diffusive wave in viscoelastic media with evolving physical property. We incorporate an equivalent formulation to prove the…
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…
This overview is devoted to splitting methods, a class of numerical integrators intended for differential equations that can be subdivided into different problems easier to solve than the original system. Closely connected with this class…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
In the present manuscript, we consider the problem of dispersive wave simulation on a rotating globally spherical geometry. In this Part IV, we focus on numerical aspects while the model derivation was described in Part III. The algorithm…
In the present article we consider the problem of wave interaction with a partially immersed, but floating body. We assume that the motion of the body is prescribed. The general mathematical formulation for this problem is presented in the…
The accurate and efficient representation of atmospheric dynamics remains a central challenge in numerical weather prediction. A particular difficulty arises from the strong anisotropy of the atmosphere, in which horizontal and vertical…
We consider the discretization in time of a system of parabolic stochastic partial differential equations with slow and fast components; the fast equation is driven by an additive space-time white noise. The numerical method is inspired by…
This paper introduces a novel approach for the construction of bulk--surface splitting schemes for semi-linear parabolic partial differential equations with dynamic boundary conditions. The proposed construction is based on a reformulation…
This paper presents an improved and modified partial differential equation (PDE)-based de-hazing algorithm. The proposed method combines logarithmic image processing models in a PDE formulation refined with linear filter-based operators in…
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of…
A variant of the Parareal method for highly oscillatory systems of PDEs was proposed by Haut and Wingate (2014). In that work they proved superlinear conver- gence of the method in the limit of infinite time scale separation. Their coarse…
This paper investigates a numerical probabilistic method for the solution of some semilinear stochastic partial differential equations (SPDEs in short). The numerical scheme is based on discrete time approximation for solutions of systems…
We propose a variational splitting technique for the generalized-$\alpha$ method to solve hyperbolic partial differential equations. We use tensor-product meshes to develop the splitting method, which has a computational cost that grows…
In this work we perform rigorous small noise expansions to study the impact of stochastic forcing on the behaviour of planar travelling wave solutions to reaction-diffusion equations on cylindrical domains. In particular, we use a…
We propose an Exponential DG approach for numerically solving partial differential equations (PDEs). The idea is to decompose the governing PDE operators into linear (fast dynamics extracted by linearization) and nonlinear (the remaining…
We consider an evolution equation of parabolic type in R having a travelling wave solution. We perform an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with…
Computer simulations of differential equations require a time discretization, which inhibits to identify the exact solution with certainty. Probabilistic simulations take this into account via uncertainty quantification. The construction of…
This paper develops a high-accuracy algorithm for time fractional wave problems, which employs a spectral method in the temporal discretization and a finite element method in the spatial discretization. Moreover, stability and convergence…
This paper deals with the numerical modeling of wave propagation in porous media described by Biot's theory. The viscous efforts between the fluid and the elastic skeleton are assumed to be a linear function of the relative velocity, which…