Efficient and accurate solution of the resistive magnetohydrodynamics model presents a significant challenge due to the presence of multiple length and time scales. Explicit time stepping methods introduce stringent CFL restrictions on the time step in order to maintain stability. This restriction is relieved by semi-implicit approaches, but accuracy considerations place practical limits on the...

This article is concerned with a new fourth-order implicit time-stepping scheme for the simulation of acoustic waves. For an enhanced efficiency, the new scheme is incorporated with a locally one-dimensional (LOD) procedure. Its stability and accuracy are analyzed and compared with those of the standard explicit fourth-order scheme. It has been observed from various experiments that the computa...

In this paper we develop two novel numerical methods for the partial integral differential equation arising from the valuation of an option whose underlying asset is governed by a jump diffusion process. These methods are based on a fitted finite volume method for the spatial discretization, an implicit-explicit time stepping scheme and the Crank-Nicolson time stepping method. We show that the ...

In this abstract, we present a case study in the application of a time-stepping method, unconstrained by the CFL condition, for computational acoustic wave propagation in the context of full waveform inversion. The numerical scheme is a locally one-dimensional (LOD) variant of alternating dimension implicit (ADI) method. The LOD method has a maximum time step that is restricted only by the Nyqu...

This article introduces a new fourth-order implicit time-stepping scheme for the numerical solution of the acoustic wave equation, as a variant of the conventional modified equation method. For an efficient simulation, the scheme incorporates a locally onedimensional (LOD) procedure having the splitting error of O( t4). Its stability and accuracy are compared with those of the standard explicit...

We construct and analyze fully discrete Galerkin (finite-element) methods of high order of accuracy for the numerical solution of the periodic initial-value problem for the Korteweg-de Vries equation. The methods are based on a standard space discretization using smooth periodic splines on a uniform mesh. For the time stepping, we use two schemes of third (resp. fourth) order of accuracy which ...

Transonic and supersonic flows over isolated wings and fighter-type aircraft configurations are computed through the numerical solution of the compressible Euler equations. Appropriate singlemesh topologies are used in combination with a new multigrid time-stepping scheme for solving the Euler equations. C-H or C-0 meshes are used for the isolated wing. A novel H-0 type mesh is introduced to di...

Classical alternating direction (AD) and fractional step (FS) methods for parabolic equations, based on some standard implicit time stepping procedure such as Crank-Nicolson, can have errors associated with the AD or FS perturbations that are much larger than the errors associated with the underlying time stepping procedure. We show that minor modi cations in the AD and FS procedures can virtua...