# Simple Numerical Schemes for the Korteweg-deVries Equation

## Abstract

Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves.

- Authors:

- Publication Date:

- Research Org.:
- University of Rochester, Rochester, NY (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 769392

- Report Number(s):
- DOE/SF-19460-372

TRN: US0201355

- DOE Contract Number:
- FC03-92SF19460

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 1 Dec 2000

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; KORTEWEG-DE VRIES EQUATION; FOURIER ANALYSIS; FINITE DIFFERENCE METHOD; NONLINEAR PROBLEMS; WAVE PACKETS

### Citation Formats

```
C. J. McKinstrie, and M. V. Kozlov.
```*Simple Numerical Schemes for the Korteweg-deVries Equation*. United States: N. p., 2000.
Web. doi:10.2172/769392.

```
C. J. McKinstrie, & M. V. Kozlov.
```*Simple Numerical Schemes for the Korteweg-deVries Equation*. United States. doi:10.2172/769392.

```
C. J. McKinstrie, and M. V. Kozlov. Fri .
"Simple Numerical Schemes for the Korteweg-deVries Equation". United States. doi:10.2172/769392. https://www.osti.gov/servlets/purl/769392.
```

```
@article{osti_769392,
```

title = {Simple Numerical Schemes for the Korteweg-deVries Equation},

author = {C. J. McKinstrie and M. V. Kozlov},

abstractNote = {Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves.},

doi = {10.2172/769392},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Fri Dec 01 00:00:00 EST 2000},

month = {Fri Dec 01 00:00:00 EST 2000}

}

Save to My Library

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