Existence and uniqueness of solutions for initial value problems of second order ordinary differential equations in Banach spaces

1999 ◽  
Vol 20 (3) ◽  
pp. 290-299
Author(s):  
Hong Shihuang ◽  
Hu Shigeng
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Banach Spaces ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Second Order ◽  
Initial Value ◽  
Uniqueness Of Solutions

scholarly journals The Treatment of Second Order Ordinary Differential Equations Using Equidistant One-step Block Hybrid

2019 ◽  
pp. 1-9
Author(s):  
Y. Skwame ◽  
J. Sabo ◽  
M. Mathew
Keyword(s):  
Numerical Analysis ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Second Order ◽  
Direct Solution ◽  
Block Method ◽  
Initial Value ◽  
One Step ◽  
Better Than

A general one-step hybrid block method with equidistant of order 6 has been successfully developed for the direct solution of second order IVPs in this article. Numerical analysis shows that the developed method is consistent and zero-stable which implies its convergence. The analysis of the new method is examined on two highly and mildly stiff second-order initial value problems to illustrate the efficiency of the method. It is obvious that our method performs better than the existing method within which we compare our result with. Hence, the approach is an adequate one for solving special second order IVPs.

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