WebJan 1, 2008 · In this paper, we deduce high-order error bounds for exponential operator splitting methods. The employed techniques are specific to linear differential equations of … WebJul 25, 2006 · A modification of the exponential time-differencing fourth-order Runge--Kutta method for solving stiff nonlinear PDEs is presented that solves the problem of numerical instability in the scheme as proposed by Cox and Matthews and generalizes the method to nondiagonal operators.

Higher-Order Splitting Method for Elastic Wave Propagation

WebDec 1, 1991 · The simplest method which takes into account the pressure in both steps of the splitting scheme is considered, yielding a fourth order accuracy in space with an optimal treatment of the boundary conditions (without error on the velocity) which could be extended to more general splitting. 6 Highly Influenced WebDec 1, 1991 · High-order splitting/spectral element methods combine accuracy in space and time, and flexibility in geometry, and thus can be very efficient in direct simulations of … lynette crimo facebook

High-order splitting methods for the incompressible Navier-Stokes ...

WebThis new way of understanding splitting methods is inspired by, but does not use, rough path theory. We show that when the driving piecewise linear path matches certain iterated stochastic integrals of Brownian motion, then a high order splitting method can be obtained. WebTo build high order explicit methods, we further note that the -dependence and -dependence in this (,) are product-separable, 2nd and 3rd order explicit symplectic algorithms can be … WebJul 28, 2009 · Since high-order splitting methods with real time are known to involve large and/or negative time steps, which destabilizes the overall procedure, the key point of our analysis is, we develop splitting methods that use complex time steps having positive real part: going to the complex plane allows to considerably increase the accuracy, while … kinship stone