#### Filter Results:

- Full text PDF available (34)

#### Publication Year

1993

2017

- This year (2)
- Last 5 years (10)
- Last 10 years (24)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

- Marlis Hochbruck, Christian Lubich, Hubert Selhofer
- SIAM J. Scientific Computing
- 1998

- Marlis Hochbruck
- 2010

- Marlis Hochbruck, Alexander Ostermann
- SIAM J. Numerical Analysis
- 2005

The aim of this paper is to analyze explicit exponential Runge-Kutta methods for the time integration of semilinear parabolic problems. The analysis is performed in an abstract Banach space framework of sectorial operators and locally Lipschitz continuous nonlinearities. We commence by giving a new and short derivation of the classical (nonstiff) order… (More)

- Jasper van den Eshof, Marlis Hochbruck
- SIAM J. Scientific Computing
- 2006

The Lanczos method is an iterative procedure to compute an orthogonal basis for the Krylov subspace generated by a symmetric matrix A and a starting vector v. An interesting application of this method is the computation of the matrix exponential exp(−τA)v. This vector plays an important role in the solution of parabolic equations where A results from some… (More)

- Marlis Hochbruck, Christian Lubich
- Numerische Mathematik
- 1999

We study a numerical method for second-order differential equations in which high-frequency oscillations are generated by a linear part. For example, semilinear wave equations are of this type. The numerical scheme is based on the requirement that it solves linear problems with constant inhomogeneity exactly. We prove that the method admits secondorder… (More)

We propose the solution of a general Toeplitz linear system via matrix embedding and transformation in generalized Cauchy form. Some interesting results are shown in the rank deficient case.

In this paper we consider the construction, analysis, implementation and application of exponential integrators. The focus will be on two types of stiff problems. The first one is characterized by a Jacobian that possesses eigenvalues with large negative real parts. Parabolic partial differential equations and their spatial discretization are typical… (More)

In this paper we analyse a family of exponential integrators for secondorder differential equations in which high-frequency oscillations in the solution are generated by a linear part. Conditions are given which guarantee that the integrators allow second-order error bounds independent of the product of the step size with the frequencies. Our convergence… (More)

- Marlis Hochbruck, Alexander Ostermann, Julia Schweitzer
- SIAM J. Numerical Analysis
- 2008

We introduce a new class of exponential integrators for the numerical integration of large-scale systems of stiff differential equations. These so-called Rosenbrock-type methods linearize the flow in each time step and make use of the matrix exponential and related functions of the Jacobian. In contrast to standard integrators, the methods are fully… (More)

- Marlis Hochbruck, Christian Lubich
- SIAM J. Numerical Analysis
- 2003