A novel second-order nonstandard finite difference method for solving one-dimensional autonomous dynamical systems

05/31/2021
by   Manh Tuan Hoang, et al.
0

In this work, a novel second-order nonstandard finite difference (NSFD) method that preserves simultaneously the positivity and local asymptotic stability of one-dimensional autonomous dynamical systems is introduced and analyzed. This method is based on novel non-local approximations for right-hand side functions of differential equations in combination with nonstandard denominator functions. The obtained results not only resolve the contradiction between the dynamic consistency and high-order accuracy of NSFD methods but also improve and extend some well-known results that have been published recently in [Applied Mathematics Letters 112(2021) 106775], [AIP Conference Proceedings 2302(2020) 110003] and [Applied Mathematics Letters 50(2015) 78-82]. Furthermore, as a simple but important application, we apply the constructed NSFD method for solving the logistic, sine, cubic, and Monod equations; consequently, the NSFD schemes constructed in the earlier work [Journal of Computational and Applied Mathematics 110(1999) 181-185] are improved significantly. Finally, we report some numerical experiments to support and illustrate the theoretical assertions as well as advantages of the constructed NSFD method.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

01/17/2020

Frequency- and Time-Limited Balanced Truncation for Large-Scale Second-Order Systems

Considering the use of dynamical systems in practical applications, ofte...
02/11/2020

A numerical damped oscillator approach to constrained Schrödinger equations

This article explains and illustrates the use of a set of coupled dynami...
06/05/2021

Second-order finite difference approximations of the upper-convected time derivative

In this work, new finite difference schemes are presented for dealing wi...
11/24/2021

Solving cubic matrix equations arising in conservative dynamics

In this paper we consider the spatial semi-discretization of conservativ...
12/28/2020

A High-Order Harmonic Balance Method for Systems With Distinct States

A pure frequency domain method for the computation of periodic solutions...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.