Analytical and numerical stability of nonlinear neutral delay integro-differential equations

Stability Analysis of One-Leg Methods for Nonlinear Neutral Delay Integrodifferential Equations

“…For problems of the class D( , 1 , 2 , 3 , , ), Hu and Huang derived the following stability results (see [9]).…”

“…For the nonlinear NDIDEs (1), Yu and Li [8] discussed the global stability and asymptotic stability of ( , ) algebraically stable Runge-Kutta methods. Recently, Hu and Huang [9] considered the analytical and numerical stability of nonlinear NDIDEs. Sufficient conditions for the analytical stability of nonlinear NDIDEs are derived, and they proved that anystable linear multistep method can preserve the asymptotic stability of the analytical solution of nonlinear NDIDEs (1).…”

Dynamic analysis of a class of neutral delay model based on the Runge-Kutta algorithm

“…We have obtained the oscillation criterion of the second-order neutral delay nonlinear differential equation model. Most of the literature mainly studied the situation α ≥ β [5][6][7][8][13][14][15][16][17][18][19][20][21]. We not only studied the situation α ≥ β but also studied the situation α < β.…”

“…However, some measures need to be taken to suppress the deviation, so the implementation principle is more complex [4]. In recent years, due to the widespread application of neutral delay differential equations in engineering cybernetics and physics fields, a wide range of attention has been drawn from scholars both at home and abroad [5][6][7][8]. With the further improvement of the Runge-Kutta algorithm and the further development of the neutral delay differential equation theory, many scholars have studied the delay differential equations and get some related results about oscillation [9][10][11][12][13][14].…”

A Modified 3-Point Adams Block Method of the Variable Step Size Strategy for Solving Neutral Delay Differential Equations

“…The Neutral Functional Differential Equations (NFDEs) numerical solution is studied by Hu et al [10] using linear multistep methods (LMM). The analytical and numerical stability of the nonlinear neutral delay-integral differential equations was studied by P. Hu and C. Huang [11]. An approximate solution for NFNDEs was also obtained by Wang and Li [12] using numerical methods, namely the one-leg θ methods.…”