scholarly journals The Simulation of One-Step Algorithms for Treating Higher Order Initial Value Problems

2021 ◽  
pp. 34-47
Author(s):  
J. Sabo ◽  
A. M. Ayinde ◽  
A. A. Ishaq ◽  
G. Ajileye
Keyword(s):  
Power Series ◽  
Initial Value Problems ◽  
Basic Function ◽  
Higher Order ◽  
Initial Value ◽  
New Approach ◽  
Basic Properties ◽  
One Step ◽  
Linear Problems

The simulation of one-step methods using interpolation and collocation for the treatment of higher order initial value problems is proposed in this paper. The new approach is derived using interpolation and collocation as a basic function through power series polynomial, where the basic properties are also analyzed. The derived method is used to treat some highly stiff linear problems. The new approach compute clearly showed that the method is reliable, efficient and gives faster convergence when compared with those in literature.

scholarly journals Hybrid Third Derivative Block Method for the Solution of General Second Order Initial Value Problems with Generalized One Step Point

2019 ◽  
Vol 12 (3) ◽  
pp. 1199-1214
Author(s):  
Ra'ft Abdelrahim ◽  
Z. Omar ◽  
O. Ala’yed ◽  
B. Batiha
Keyword(s):  
Power Series ◽  
Convergence Analysis ◽  
Initial Value Problem ◽  
Initial Value Problems ◽  
Numerical Procedure ◽  
Second Order ◽  
Block Method ◽  
Initial Value ◽  
One Step ◽  
Third Derivative

This paper deals with two-step hybrid block method with one generalized off-step points for solving second order initial value problem. In derivation of this method, power series of order nine are interpolated at the first two step points while its second and third derivatives are collocated at all point in the selected interval. The new developed method is employed to solve several problems of second order initial value problems. Convergence analysis of the new method alongside numerical procedure is established. The performance of the proposed method is found to be more accurate than existing method available in the literature when solving the same problems.

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
Sign in / Sign up

Export Citation Format

Share Document