High-order splitting schemes for semilinear evolution equations

High-order splitting schemes for semilinear evolution equations

We first derive necessary and sufficient stiff order conditions, up to order four, for exponential splitting schemes applied to semilinear evolution equations. The main idea is to identify the local splitting error as a sum of quadrature errors. The order conditions of the quadrature rules then yield the stiff order conditions in an explicit fashion, similarly to that of Runge–Kutta schemes. Fu...

Towards High-Order Fluctuation-Splitting Schemes for Navier-Stokes Equations

This paper reports progress towards high-order fluctuation-splitting schemes for the Navier-Stokes Equations. High-order schemes we examined previously are all based on gradient reconstruction, which may result in undesired mesh-dependency problem due to the somewhat ambiguous gradient reconstruction procedures. Here, we consider schemes for P2 elements in order to eliminate the need for such g...

High Order Compact Finite Difference Schemes for Solving Bratu-Type Equations

In the present study, high order compact finite difference methods is used to solve one-dimensional Bratu-type equations numerically. The convergence analysis of the methods is discussed and it is shown that the theoretical order of the method is consistent with its numerical rate of convergence. The maximum absolute errors in the solution at grid points are calculated and it is shown that the ...

High Order Schemes for Wave Equations

The continuous and discontinuous Galerkin time stepping methodologies are combined to develop approximations of second order time derivatives of arbitrary order. This eliminates the doubling of the number of variables that results when a second order problem is written as a first order system. Stability, convergence, and accuracy, of these schemes is established in the context of the wave equat...

Semilinear Evolution Equations of Second Order via Maximal Regularity