Nonstandard finite difference schemes for linear and non-linear Fokker–Planck equations

IF 1.4 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

Journal of Engineering Mathematics Pub Date : 2024-03-23 DOI:10.1007/s10665-024-10346-2

A. S. Neena, Dominic P. Clemence-Mkhope, Ashish Awasthi

引用次数: 0

Abstract

The goal of this paper is to develop a nonstandard finite difference-based numerical technique for solving the one-dimensional linear and non-linear Fokker–Planck equations. Characteristics of the nonstandard finite difference method are presented to understand the development of the proposed method. Conditions for the dynamic consistency of positivity and stability of the schemes are obtained. Numerical experiments have been carried out to demonstrate the competitiveness of the proposed methods in comparison to some existing standard methods. In support of the proposed method and analysis, the \(l_2\) and \(l_\infty \) errors are also presented.

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线性和非线性福克-普朗克方程的非标准有限差分方案

本文旨在开发一种基于非标准有限差分的数值技术，用于求解一维线性和非线性福克-普朗克方程。本文介绍了非标准有限差分法的特点，以便理解所提议方法的发展。此外，还提出了方案正负动态一致性和稳定性的条件。通过数值实验证明了所提方法与一些现有标准方法的竞争力。为了支持所提出的方法和分析，还提出了 \(l_2\) 和 \(l\infty \) 误差。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Engineering Mathematics 工程技术-工程：综合

CiteScore

2.10

自引率

7.70%

发文量

审稿时长

6 months

期刊介绍： The aim of this journal is to promote the application of mathematics to problems from engineering and the applied sciences. It also aims to emphasize the intrinsic unity, through mathematics, of the fundamental problems of applied and engineering science. The scope of the journal includes the following: • Mathematics: Ordinary and partial differential equations, Integral equations, Asymptotics, Variational and functional−analytic methods, Numerical analysis, Computational methods. • Applied Fields: Continuum mechanics, Stability theory, Wave propagation, Diffusion, Heat and mass transfer, Free−boundary problems; Fluid mechanics: Aero− and hydrodynamics, Boundary layers, Shock waves, Fluid machinery, Fluid−structure interactions, Convection, Combustion, Acoustics, Multi−phase flows, Transition and turbulence, Creeping flow, Rheology, Porous−media flows, Ocean engineering, Atmospheric engineering, Non-Newtonian flows, Ship hydrodynamics; Solid mechanics: Elasticity, Classical mechanics, Nonlinear mechanics, Vibrations, Plates and shells, Fracture mechanics; Biomedical engineering, Geophysical engineering, Reaction−diffusion problems; and related areas. The Journal also publishes occasional invited ''Perspectives'' articles by distinguished researchers reviewing and bringing their authoritative overview to recent developments in topics of current interest in their area of expertise. Authors wishing to suggest topics for such articles should contact the Editors-in-Chief directly. Prospective authors are encouraged to consult recent issues of the journal in order to judge whether or not their manuscript is consistent with the style and content of published papers.