用两种无网格方法求解非线性 Fisher-Kolmogorov-Petrovsky-Piskunov 方程

IF 2.8 3区工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Computational Particle Mechanics Pub Date : 2024-07-16 DOI:10.1007/s40571-024-00794-z

J. J. Benito, A. García, M. Negreanu, F. Ureña, A. M. Vargas

{"title":"用两种无网格方法求解非线性 Fisher-Kolmogorov-Petrovsky-Piskunov 方程","authors":"J. J. Benito, A. García, M. Negreanu,  F. Ureña, A. M. Vargas","doi":"10.1007/s40571-024-00794-z","DOIUrl":null,"url":null,"abstract":"<div><p>This paper explores the numerical solution of the Fisher–Kolmogorov–Petrovsky–Piskunov (FKPP) equation through two meshless methods: a space–time cloud method and an explicit method employing generalized finite difference formulas (GFDM). The efficacy of the space–time cloud method in addressing this equation is demonstrated, and a comparative analysis with the results obtained from the explicit method using GFDM is conducted. The findings suggest that the space–time finite difference method delivers precise and stable solutions for the Fisher–KPP equation.</p></div>","PeriodicalId":524,"journal":{"name":"Computational Particle Mechanics","volume":"11 6","pages":"2373 - 2379"},"PeriodicalIF":2.8000,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Solving nonlinear Fisher–Kolmogorov–Petrovsky–Piskunov equation using two meshless methods\",\"authors\":\"J. J. Benito, A. García, M. Negreanu,  F. Ureña, A. M. Vargas\",\"doi\":\"10.1007/s40571-024-00794-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper explores the numerical solution of the Fisher–Kolmogorov–Petrovsky–Piskunov (FKPP) equation through two meshless methods: a space–time cloud method and an explicit method employing generalized finite difference formulas (GFDM). The efficacy of the space–time cloud method in addressing this equation is demonstrated, and a comparative analysis with the results obtained from the explicit method using GFDM is conducted. The findings suggest that the space–time finite difference method delivers precise and stable solutions for the Fisher–KPP equation.</p></div>\",\"PeriodicalId\":524,\"journal\":{\"name\":\"Computational Particle Mechanics\",\"volume\":\"11 6\",\"pages\":\"2373 - 2379\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2024-07-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Particle Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40571-024-00794-z\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Particle Mechanics","FirstCategoryId":"5","ListUrlMain":"https://link.springer.com/article/10.1007/s40571-024-00794-z","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}

引用次数: 0

摘要

本文通过两种无网格方法：时空云方法和采用广义有限差分公式（GFDM）的显式方法，探讨了Fisher-Kolmogorov-Petrovsky-Piskunov （FKPP）方程的数值解。论证了时空云方法求解该方程的有效性，并与使用GFDM的显式方法得到的结果进行了比较分析。研究结果表明，时空有限差分方法为Fisher-KPP方程提供了精确和稳定的解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Solving nonlinear Fisher–Kolmogorov–Petrovsky–Piskunov equation using two meshless methods

查看原文本刊更多论文

Solving nonlinear Fisher–Kolmogorov–Petrovsky–Piskunov equation using two meshless methods

This paper explores the numerical solution of the Fisher–Kolmogorov–Petrovsky–Piskunov (FKPP) equation through two meshless methods: a space–time cloud method and an explicit method employing generalized finite difference formulas (GFDM). The efficacy of the space–time cloud method in addressing this equation is demonstrated, and a comparative analysis with the results obtained from the explicit method using GFDM is conducted. The findings suggest that the space–time finite difference method delivers precise and stable solutions for the Fisher–KPP equation.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Computational Particle Mechanics Mathematics-Computational Mathematics

CiteScore

5.70

自引率

9.10%

发文量

期刊介绍： GENERAL OBJECTIVES: Computational Particle Mechanics (CPM) is a quarterly journal with the goal of publishing full-length original articles addressing the modeling and simulation of systems involving particles and particle methods. The goal is to enhance communication among researchers in the applied sciences who use "particles'''' in one form or another in their research. SPECIFIC OBJECTIVES: Particle-based materials and numerical methods have become wide-spread in the natural and applied sciences, engineering, biology. The term "particle methods/mechanics'''' has now come to imply several different things to researchers in the 21st century, including: (a) Particles as a physical unit in granular media, particulate ﬂows, plasmas, swarms, etc., (b) Particles representing material phases in continua at the meso-, micro-and nano-scale and (c) Particles as a discretization unit in continua and discontinua in numerical methods such as Discrete Element Methods (DEM), Particle Finite Element Methods (PFEM), Molecular Dynamics (MD), and Smoothed Particle Hydrodynamics (SPH), to name a few.