One-step hybrid block method with one generalized off-step points for direct solution of second order ordinary differential equations

2016 ◽  
Vol 10 ◽  
pp. 1423-1432
Author(s):  
Ra'ft Abdelrahim ◽  
Zurni Omar
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Direct Solution ◽  
Block Method ◽  
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.

DERIVATION AND IMPLEMENTATION OF A THREE-STEP HYBRID BLOCK ALGORITHM (TSHBA) FOR DIRECT SOLUTION OF LINEAR AND NONLINEAR SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 4 (4) ◽  
pp. 477-483
Author(s):  
O. E. Abolarin ◽  
B. G. Ogunware ◽  
A. F. Adebisi ◽  
S. O. Ayinde
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Conditions ◽  
Multistep Method ◽  
Second Order ◽  
Direct Solution ◽  
Block Method ◽  
Order Error ◽  
Block Algorithm ◽  
Grid Points

The development and application of an implicit hybrid block method for the direct solution of second order ordinary differential equations with given initial conditions is shown in this research. The derivation of the three-step scheme was done through collocation and interpolation of power series approximation to give a continuous linear multistep method. The evaluation of the continuous method at the grid and off grid points formed the discrete block method. The basic properties of the method such as order, error constant, zero stability, consistency and convergence were properly examined. The new block method produced more accurate results when compared with similar works carried out by existing authors on the solution of linear and non-linear second order ordinary differential equations

scholarly journals Three-Step Two-Hybrid Block Method for the Direct Solution of Second-Order Ordinary Differential Equations

2020 ◽  
pp. 15-23
Author(s):  
Raymond Dominic ◽  
Kyagya Yusuf T.
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Basic Function ◽  
Second Order ◽  
Direct Solution ◽  
Block Method ◽  
Stiff Equations ◽  
Two Hybrid

In this paper a three-step two hybrid block method with two offgrid hybrid points chosen within interval [Xn,Xn+1] and [Xn+1,Xn+2] was developed to solve second Order Ordinary Differential Equations directly, using the power series as the basic function to approximate and generate some continuous schemes. The basic properties of the method was investigated and was found to converge. Numerical Solution of our method was tested on some stiff equations and was found to give better approximation than the existing method.

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