It is shown that the solutions of the pure initial-value problem for the KP and regularized KP equations are the same, within the order of accuracy attributable to either, on the time scale 0 ≤ t ≤ −3/2 , during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles. under the Creative Commons Attribution License, which permits unrest...

The Computational Singular Perturbation CSP method of Lam and Goussis is an iterative method to reduce the dimensionality of systems of ordinary di erential equations with multiple time scales In J Nonlin Sci to appear the authors showed that each iteration of the CSP algorithm improves the approxima tion of the slow manifold by one order In this paper it is shown that the CSP method simultaneo...

In this paper we develop non-linear ADER schemes for time-dependent scalar linear and non-linear conservation laws in one, two and three space dimensions. Numerical results of schemes of up to fifth order of accuracy in both time and space illustrate that the designed order of accuracy is achieved in all space dimensions for a fixed Courant number and essentially non-oscillatory results are obt...

Many geophysical flows are merely perturbations of some fundamental equilibrium state. If a numerical scheme shall capture such flows efficiently, it should be able to preserve the unperturbed equilibrium state at the discrete level. Here we present a class of schemes of any desired order of accuracy which preserve the lake at rest perfectly. These schemes should have an impact for studying imp...

In this paper we analyze the consistency and stability properties of Runge-Kutta discrete adjoints. Discrete adjoints are very popular in optimization and control since they can be constructed automatically by reverse mode automatic differentiation. The consistency analysis uses the concept of elementary differentials and reveals that the discrete Runge-Kutta adjoint method has the same order o...

Including derivative information in the modelling of moving interfaces has been proposed as one method to increase the accuracy of numerical schemes with minimal additional cost. Here a new level set reinitialization technique using the fast marching method is presented. This augmented fast marching method will calculate the signed distance function and up to the secondorder derivatives of the ...

This paper investigates the temporal accuracy of the velocity and pressure when explicit Runge–Kutta methods are applied to the incompressible Navier–Stokes equations. It is shown that, at least up to and including fourth order, the velocity attains the classical order of accuracy without further constraints. However, in case of a time-dependent gradient operator, which can appear in case of ti...

We introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then present a systematic procedure based on the framework of modified differential equations for the construction of stochastic integrators that cap...

Empathic accuracy (EA)-the correct assessment of the affective states and thoughts of a social partner-affects social behavior and the outcome of interpersonal interactions. Growing evidence has shown that interpersonal power of a perceiver affects EA when assessing a target. This picture, however, is not obvious; there is evidence supporting both the idea that power can improve EA or impair it...

We propose and analyze spectral direction splitting schemes for the incompressible Navier-Stokes equations. The schemes combine a Legendre-spectral method for the spatial discretization and a pressure-stabilization/direction splitting scheme for the temporal discretization, leading to a sequence of one-dimensional elliptic equations at each time step while preserving the same order of accuracy ...