articleActa NumericaMay 1, 2010GREEN OA

Exponential integrators

MHMarlis HochbruckAOAlexander Ostermann

Karlsruhe Institute of Technology · Universität Innsbruck

Indexed incrossrefdatacite

Abstract

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 examples. The second class consists of highly oscillatory problems with purely imaginary eigenvalues of large modulus. Apart from motivating the construction of exponential integrators for various classes of problems, our main intention in this article is to present the mathematics behind these methods. We will derive error bounds that are independent of stiffness…

Citation impact

1,018
total citations
FWCI
33.82
Percentile
100%
References
128
Citations per year

Authors

2

Topics & keywords

Topics
Keywords
  • Exponential integrator
  • Exponential function
  • Integrator
  • Eigenvalues and eigenvectors
  • Discretization
  • Jacobian matrix and determinant
  • Mathematics
  • Applied mathematics
No related works found for this paper.

Funding