Initial-value problems: one-step methods

1987 ◽  
pp. 42-77
Author(s):  
L. Fox ◽  
D. F. Mayers
Keyword(s):  
Initial Value Problems ◽  
Initial Value ◽  
One Step

scholarly journals New explicit high‐order one‐step methods for singular initial value problems

2020 ◽  
Author(s):  
Bohdan Datsko ◽  
Myroslaw Kutniv ◽  
Andriy Kunynets ◽  
Andrzej Włoch
Keyword(s):  
Initial Value Problems ◽  
High Order ◽  
Initial Value ◽  
One Step

A Nonlinear Explicit One-Step Integration Scheme for Singular Autonomous Initial Value Problems

2007 ◽  
Author(s):  
Higinio Ramos ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Initial Value Problems ◽  
Integration Scheme ◽  
Initial Value ◽  
One Step

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.

scholarly journals Numerical Simulation of One Step Block Method for Treatment of Second Order Forced Motions in Mass-Spring Systems

2021 ◽  
pp. 1-11
Author(s):  
J. Sabo ◽  
T. Y. Kyagya ◽  
W. J. Vashawa
Keyword(s):  
Numerical Simulation ◽  
Initial Value Problems ◽  
Second Order ◽  
Block Method ◽  
Initial Value ◽  
Mathematical Problems ◽  
One Step ◽  
Grid Points ◽  
The One ◽  
Mass Spring

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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