scholarly journals Variable-order, variable-step methods for second-order initial-value problems

1997 ◽  
Vol 79 (2) ◽  
pp. 263-276 ◽  
Author(s):  
M.S.H. Khiyal ◽  
R.M. Thomas
Keyword(s):  
Initial Value Problems ◽  
Second Order ◽  
Variable Order ◽  
Initial Value ◽  
Variable Step ◽  
Order Variable

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.

Solving Directly Second Order Initial Value Problems with Lucas Polynomial

2019 ◽  
pp. 1-7
Author(s):  
A. O. Adeniran ◽  
I. O. Longe
Keyword(s):  
Initial Value Problems ◽  
Numerical Scheme ◽  
Second Order ◽  
Numerical Implementation ◽  
Hybrid Scheme ◽  
Initial Value ◽  
Variable Step ◽  
Interpolation Technique ◽  
One Step ◽  
Order Four

Aims/ Objectives: This paper presents a one step hybrid numerical scheme with one o gridpoints for solving directly the general second order initial value problems.Study Design: Section one which is the introduction, give a brief about initial value problem.In the next section derivation of one step hybrid scheme is considered. Section Three providesthe analysis of the scheme, while numerical implementation of the scheme and conclusion are inSections four and ve respectively.Methodology: The scheme is developed using collocation and interpolation technique invokedon Lucas polynomial.Results: The proposed scheme is consistent, zero stable and of order four and can estimate theapproximate solution at both step and o step points simultaneously by using variable step size.Conclusion: Numerical results are given to show the eciency of the proposed scheme over someexisting schemes of same and higher order[ [1],[2], [3],[4], [5], [6]].

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