Abstract The main goal of this paper is to developed a high-order and accurate method for the solution one-dimensional generalized Burgers-Fisher with Numman boundary conditions. We combined between fourth-order compact finite difference scheme spatial part diagonal implicit Runge Kutta in temporal part. In addition, we discretized points by using terms fourth order accuracy. This combine leads...

preprint numerics no. 7/2011 norwegian university of science and technology trondheim, norway Direct applications of high order DIRK-CF methods as presented in [7] to the incompressible Navier-Stokes equations were found to yield a loss in order of convergence. The DIRK-CF methods are exponential integrators arising from the IMEX Runge-Kutta techniques proposed in [1], and are semi-Lagrangian w...

Variable-step (VS) second derivative $k$-step $3$-stage Hermite--Birkhoff--Obrechkoff (HBO) methods of order $p=(k+3)$, denoted by HBO$(p)$ are constructed as a combination of linear $k$-step methods of order $(p-2)$ and a second derivative two-step diagonally implicit $3$-stage Hermite--Birkhoff method of order 5 (DIHB5) for solving stiff ordinary differential equations. The main reason for co...

In this work, we construct and derive a new class of exponentially fitted two-derivative diagonally implicit Runge–Kutta (EFTDDIRK) methods for the numerical solution differential equations with oscillatory solutions. First, general format so-called modified (TDDIRK) is proposed. Their order conditions up to six are derived by introducing set bi-colored rooted trees deriving elementary weights....

The potential of the hybridized discontinuous Galerkin (HDG) method has been recognized for the computation of stationary flows. Extending the method to instationary problems can, e.g., be done by backward difference formulae (BDF) or diagonally implicit Runge-Kutta (DIRK) methods. In this publication, we investigate the use of embedded DIRK methods in an HDG solver, including the use of adapti...

This is an extended version of the talk given by the first author at the conference. We report on the outcome of some experiments with the decomposition of products of (generalized) characters of some classical groups. In particular some results of the PhD-thesis of Dirk Mattig on the products of unipotent characters of general linear groups are presented and commented. In order to obtain simil...

The present study is focused on the application of two families implicit time-integration schemes for general time-dependent balance laws convection-diffusion-reaction type discretized by a hybridized discontinuous Galerkin method in space, namely backward differentiation formulas (BDF) and diagonally Runge-Kutta (DIRK) methods. Special attention devoted to embedded DIRK methods, which allow in...