Stability of explicit and diagonal implicit Runge–Kutta methods for nonlinear Volterra functional differential equations in Banach spaces

2006 ◽  
Vol 183 (1) ◽  
pp. 68-78 ◽  
Author(s):  
Liping Wen ◽  
Yuexin Yu ◽  
Shoufu Li
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Functional Differential Equations ◽  
Runge Kutta ◽  
Functional Differential

scholarly journals Approximation methods and the generalised Fuller index for semi-flows in Banach spaces

1986 ◽  
Vol 29 (3) ◽  
pp. 299-308 ◽  
Author(s):  
A. J. B. Potter
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Solutions ◽  
Banach Spaces ◽  
Functional Differential Equations ◽  
Periodic Points ◽  
Approximation Methods ◽  
Functional Differential ◽  
Linear Differential ◽  
Fuller Index

In [3] Fuller introduced an index (now called the Fuller index) in order to study periodic solutions of ordinary differential equations. The objective of this paper is to give a simple generalisation of the Fuller index which can be used to study periodic points of flows in Banach spaces. We do not claim any significant breakthrough but merely suggest that the simplistic approach, presented here, might prove useful for the study of non-linear differential equations. We show our results can be used to study functional differential equations.

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