dorsal/arxiv
View SchemaA Second-Order Stochastic Leap-Frog Algorithm for Langevin Simulation
| Authors | Ji Qiang, Salman Habib |
|---|---|
| Categories | |
| ArXiv ID | physics/0008196 |
| URL | https://arxiv.org/abs/physics/0008196 |
| Journal | eConf C000821 (2000) MOA20 |
Abstract
Langevin simulation provides an effective way to study collisional effects in beams by reducing the six-dimensional Fokker-Planck equation to a group of stochastic ordinary differential equations. These resulting equations usually have multiplicative noise since the diffusion coefficients in these equations are functions of position and time. Conventional algorithms, e.g. Euler and Heun, give only first order convergence of moments in a finite time interval. In this paper, a stochastic leap-frog algorithm for the numerical integration of Langevin stochastic differential equations with multiplicative noise is proposed and tested. The algorithm has a second-order convergence of moments in a finite time interval and requires the sampling of only one uniformly distributed random variable per time step. As an example, we apply the new algorithm to the study of a mechanical oscillator with multiplicative noise.
{
"annotation_id": "3ae8599e-0450-4270-bf27-5604fe00afea",
"date_created": "2026-03-02T18:00:32.174000Z",
"date_modified": "2026-03-02T18:00:32.174000Z",
"file_hash": "2b89caed22eaf71aac096fe8fc37dd1eda637ec4787411c56573c81f74d3a36f",
"private": false,
"record": {
"abstract": "Langevin simulation provides an effective way to study collisional effects in\nbeams by reducing the six-dimensional Fokker-Planck equation to a group of\nstochastic ordinary differential equations. These resulting equations usually\nhave multiplicative noise since the diffusion coefficients in these equations\nare functions of position and time. Conventional algorithms, e.g. Euler and\nHeun, give only first order convergence of moments in a finite time interval.\nIn this paper, a stochastic leap-frog algorithm for the numerical integration\nof Langevin stochastic differential equations with multiplicative noise is\nproposed and tested. The algorithm has a second-order convergence of moments in\na finite time interval and requires the sampling of only one uniformly\ndistributed random variable per time step. As an example, we apply the new\nalgorithm to the study of a mechanical oscillator with multiplicative noise.",
"arxiv_id": "physics/0008196",
"authors": [
"Ji Qiang",
"Salman Habib"
],
"categories": [
"physics.acc-ph"
],
"journal_ref": "eConf C000821 (2000) MOA20",
"title": "A Second-Order Stochastic Leap-Frog Algorithm for Langevin Simulation",
"url": "https://arxiv.org/abs/physics/0008196"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "c45d2788-9fd7-4d9b-bee6-db8a43241c02",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}