A general [L, M] one-step integrator for initial value problems

2010 ◽  
Vol 88 (2) ◽  
pp. 348-359
Author(s):  
U. S.U. Aashikpelokhai
Author(s):  
Bohdan Datsko ◽  
Myroslaw Kutniv ◽  
Andriy Kunynets ◽  
Andrzej Włoch

2007 ◽  
Author(s):  
Higinio Ramos ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras

Author(s):  
Y. Skwame ◽  
J. Sabo ◽  
M. Mathew

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.


Author(s):  
J. Sabo ◽  
T. Y. Kyagya ◽  
W. J. Vashawa

This paper discuss the numerical simulation of one step block method for treatment of second order forced motions in mass-spring systems of initial value problems. The one step block method has been developed with the introduction of off-mesh point at both grid and off- grid points using interpolation and collocation procedure to increase computational burden which may jeopardize the accuracy of the method in terms of error. The basic properties of the one step block method was established and numerical analysis shown that the one step block method was found to be consistent, convergent and zero-stable. The one step block method was simulated on three highly stiff mathematical problems to validate the accuracy of the block method without reduction, and obviously the results shown are more accurate over the existing method in literature.


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