A Variable Step Runge--Kutta--Nyström Integrator for Reversible Systems of Second Order Initial Value Problems

2005 ◽  
Vol 26 (3) ◽  
pp. 963-978 ◽  
Author(s):  
J. R. Cash
Keyword(s):  
Initial Value Problems ◽  
Second Order ◽  
Reversible Systems ◽  
Initial Value ◽  
Variable Step ◽  
Runge Kutta

Superstable implicit Runge-Kutta methods for second order initial value problems

1989 ◽  
Vol 29 (3) ◽  
pp. 518-526
Author(s):  
R. K. Jain ◽  
Rajive Kumar ◽  
Rakesh Goel
Keyword(s):  
Initial Value Problems ◽  
Second Order ◽  
Initial Value ◽  
Runge Kutta

scholarly journals Half Step Numerical Method for Solution of Second Order Initial Value Problems

2021 ◽  
pp. 77-81
Author(s):  
Adeniran Adebayo O. ◽  
Edaogbogun Kikelomo
Keyword(s):  
Numerical Method ◽  
Initial Value Problems ◽  
Second Order ◽  
Variable Step Size ◽  
Initial Value ◽  
Step Size ◽  
Stable Order ◽  
Variable Step ◽  
Interpolation Technique ◽  
Order Four

This paper presents a half step numerical method for solving directly general second order initial value problems. The scheme is developed via collocation and interpolation technique invoked on power series polynomial. The proposed method is consistent, zero stable, order four and three. This method can estimate the approximate solution at both step and off step points simultaneously by using variable step size. Numerical results are given to show the efficiency of the proposed scheme over some existing schemes of same and higher order.

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