# Iterated Crank-Nicolson method for hyperbolic and parabolic equations in numerical relativity

## Abstract

The iterated Crank-Nicolson is a predictor-corrector algorithm commonly used in numerical relativity for the solution of both hyperbolic and parabolic partial differential equations. We here extend the recent work on the stability of this scheme for hyperbolic equations by investigating the properties when the average between the predicted and corrected values is made with unequal weights and when the scheme is applied to a parabolic equation. We also propose a variant of the scheme in which the coefficients in the averages are swapped between two corrections leading to systematically larger amplification factors and to a smaller numerical dispersion.

- Authors:

- Department of Physics, Udine University, Udine (Italy)
- (Germany)
- Max-Planck-Institut fuer Gravitationsphysik, Albert Einstein Institut, Golm (Germany)
- (Italy)
- (United States)

- Publication Date:

- OSTI Identifier:
- 20776739

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 73; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.73.044001; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; ALGORITHMS; AMPLIFICATION; CORRECTIONS; COSMOLOGY; GENERAL RELATIVITY THEORY; ITERATIVE METHODS; MATHEMATICAL SOLUTIONS; PARTIAL DIFFERENTIAL EQUATIONS; STABILITY

### Citation Formats

```
Leiler, Gregor, Max-Planck-Institut fuer Gravitationsphysik, Albert Einstein Institut, Golm, Rezzolla, Luciano, SISSA, International School for Advanced Studies and INFN, Trieste, and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001.
```*Iterated Crank-Nicolson method for hyperbolic and parabolic equations in numerical relativity*. United States: N. p., 2006.
Web. doi:10.1103/PhysRevD.73.044001.

```
Leiler, Gregor, Max-Planck-Institut fuer Gravitationsphysik, Albert Einstein Institut, Golm, Rezzolla, Luciano, SISSA, International School for Advanced Studies and INFN, Trieste, & Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001.
```*Iterated Crank-Nicolson method for hyperbolic and parabolic equations in numerical relativity*. United States. doi:10.1103/PhysRevD.73.044001.

```
Leiler, Gregor, Max-Planck-Institut fuer Gravitationsphysik, Albert Einstein Institut, Golm, Rezzolla, Luciano, SISSA, International School for Advanced Studies and INFN, Trieste, and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001. Wed .
"Iterated Crank-Nicolson method for hyperbolic and parabolic equations in numerical relativity". United States.
doi:10.1103/PhysRevD.73.044001.
```

```
@article{osti_20776739,
```

title = {Iterated Crank-Nicolson method for hyperbolic and parabolic equations in numerical relativity},

author = {Leiler, Gregor and Max-Planck-Institut fuer Gravitationsphysik, Albert Einstein Institut, Golm and Rezzolla, Luciano and SISSA, International School for Advanced Studies and INFN, Trieste and Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001},

abstractNote = {The iterated Crank-Nicolson is a predictor-corrector algorithm commonly used in numerical relativity for the solution of both hyperbolic and parabolic partial differential equations. We here extend the recent work on the stability of this scheme for hyperbolic equations by investigating the properties when the average between the predicted and corrected values is made with unequal weights and when the scheme is applied to a parabolic equation. We also propose a variant of the scheme in which the coefficients in the averages are swapped between two corrections leading to systematically larger amplification factors and to a smaller numerical dispersion.},

doi = {10.1103/PhysRevD.73.044001},

journal = {Physical Review. D, Particles Fields},

number = 4,

volume = 73,

place = {United States},

year = {Wed Feb 15 00:00:00 EST 2006},

month = {Wed Feb 15 00:00:00 EST 2006}

}

Other availability

Save to My Library

You must Sign In or Create an Account in order to save documents to your library.