Related papers: Higher order A-stable schemes for the wave equatio…
In ordinary turbulence research it has been a long standing tradition to solve the equations in spectral space giving the best possible accuracy. This is indeed a natural choice for incompressible problems with periodic boundaries, but it…
This paper is concerned with moving mesh finite difference solution of partial differential equations. It is known that mesh movement introduces an extra convection term and its numerical treatment has a significant impact on the stability…
We consider quadrature formulas of high order in time based on Radau-type, L-stable implicit Runge-Kutta schemes to solve time dependent stiff PDEs. Instead of solving a large nonlinear system of equations, we develop a method that performs…
We introduce a discrete scheme for second order fully nonlinear parabolic PDEs with Caputo's time fractional derivatives. We prove the convergence of the scheme in the framework of the theory of viscosity solutions. The discrete scheme can…
We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the…
In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii equation with angular momentum rotation in three dimensions. Based on the idea of the scalar…
This work considers two boundary correction techniques to mitigate the reduction in the temporal order of convergence in PDE sense (i.e., when both the space and time resolutions tend to zero independently of each other) of $d$ dimension…
We present a second-order-in-time finite difference scheme for the Cahn-Hilliard-Hele-Shaw equations. This numerical method is uniquely solvable and unconditionally energy stable. At each time step, this scheme leads to a system of…
Motivated by important applications in image processing, we study a class of second-order geometric quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems…
Domain decomposition methods are essential in solving applied problems on parallel computer systems. For boundary value problems for evolutionary equations the implicit schemes are in common use to solve problems at a new time level…
A new explicit stabilized scheme of weak order one for stiff and ergodic stochastic differential equations (SDEs) is introduced. In the absence of noise, the new method coincides with the classical deterministic stabilized scheme (or…
An important ingredient in numerical modelling of high temperature magnetised astrophysical plasmas is the anisotropic transport of heat along magnetic field lines from higher to lower temperatures.Magnetohydrodynamics (MHD) typically…
The Peaceman-Rachford alternating direction implicit (ADI) scheme for linear time-dependent Maxwell equations is analyzed on a heterogeneous cuboid. Due to discontinuities of the material parameters, the solution of the Maxwell equations is…
A novel 3-D higher-order finite-difference time-domain framework with complex frequency-shifted perfectly matched layer for the modeling of wave propagation in cold plasma is presented. Second- and fourth-order spatial approximations are…
Multitime evolution PDEs for Rayleigh waves are considered, using geometrical ingredients capable to build an ultra-parabolic-hyperbolic differential operator. Their soliton solutions are found based on appropriate hypotheses and specific…
Numerical methods for solving the ideal magnetohydrodynamic (MHD) equations in more than one space dimension must either confront the challenge of controlling errors in the discrete divergence of the magnetic field, or else be faced with…
We present a systematical approach to developing arbitrarily high order, unconditionally energy stable numerical schemes for thermodynamically consistent gradient flow models that satisfy energy dissipation laws. Utilizing the energy…
We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. We modify the classical algorithm by introducing a new…
In this paper, modulation instability and nonlinear supratransmission are investigated in a one-dimensional chain of atoms using cubic-quartic nonlinearity coefficients. As a result, we establish the discrete nonlinear evolution equation by…
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite…