Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory

1986 ◽  
Vol 24 (5) ◽  
pp. 583-601 ◽  
Author(s):  
Henjin Chi ◽  
Jonathan Bell ◽  
Brian Hassard
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Delay Differential Equation ◽  
Nerve Conduction ◽  
Conduction Theory ◽  
Delay Differential

scholarly journals Some Stability and Convergence of Additive Runge-Kutta Methods for Delay Differential Equations with Many Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Haiyan Yuan ◽  
Jingjun Zhao ◽  
Yang Xu
Keyword(s):  
Differential Equation ◽  
Numerical Solution ◽  
Convergence Analysis ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Stability And Convergence ◽  
Runge Kutta ◽  
Lagrangian Interpolation ◽  
The Stability ◽  
Delay Differential

This paper is devoted to the stability and convergence analysis of the additive Runge-Kutta methods with the Lagrangian interpolation (ARKLMs) for the numerical solution of a delay differential equation with many delays. GDN stability and D-Convergence are introduced and proved. It is shown that strongly algebraically stability gives D-Convergence DA, DAS, and ASI stability give GDN stability. Some examples are given in the end of this paper which confirms our results.

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