On a new one-step method for numerical solution of initial-value problems in ordinary differential equations

2001 ◽  
Vol 77 (3) ◽  
pp. 457-467 ◽  
Author(s):  
P. Kama ◽  
E.A. Ibijola
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Initial Value ◽  
Step Method ◽  
One Step

scholarly journals A Step Block Algorithm for Solving First Order Initial Value Problems in Ordinary Differential Equations

2017 ◽  
Vol 2 (1) ◽  
Author(s):  
Emmanuel O Adeyefa ◽  
Oluwatosin Fadaka
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Finite Difference Methods ◽  
Initial Value ◽  
Step Method ◽  
Block Algorithm ◽  
One Step ◽  
Difference Methods

The implementation of the newly formulated polynomials, ADEM-B orthogonal polynomials,  valid in the interval [-1, 1] with respect to weight function is our major focus in this work. The polynomials, which serve as basis function are employed to develop finite difference methods. Varying off-step points are considered for only One-Step method for the solution of the initial value problems of Ordinary Differential Equations (ODEs).  By selection of points for both interpolation and collocation, threeimportant class of block finite difference methods are produced. The methods are analyzed for their basic properties and findings show that they are accurate and convergent.

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.

Sign in / Sign up

Export Citation Format

Share Document