Geometric Stability Switch Criteria in HIV-1 Infection Delay Model

Monica, C.; Pitchaimani, M.

doi:10.1007/s00332-018-9481-y

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2021

2022

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“…With more and more research on delay differential equations [1][2][3][4][5], it has been widely used in various fields, such as population research [6,7], epidemiology [8,9], electrodynamics [10,11], neural network system [12,13] and so on. As a special class of delay differential equations, differential equations with piecewise constant arguments (EPCA) are difficult to solve accurately because of their complex structure.…”

Section: Introductionmentioning

confidence: 99%

Numerical Stability of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments with Matrix Coefficients

Yin

Wang

2022

Universal Journal of Mathematics and Applications

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The paper discusses the analytical stability and numerical stability of differential equations with piecewise constant arguments with matrix coefficients. It is proved that the Runge-Kutta method can keep the convergence order. The recurrence relation of the Runge-Kutta method applied to the equations is obtained. Then, the stability conditions of the numerical solution under different matrix coefficients are given by Pade approximation and order star theory. Finally, the conclusions are verified by several numerical experiments.

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