scholarly journals GENERALIZED TWO-HYBRID ONE-STEP IMPLICIT THIRD DERIVATIVE BLOCK METHOD FOR THE DIRECT SOLUTION OF SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

2017 ◽  
Vol 112 (3) ◽  
Author(s):  
M. Alkasassbeh ◽  
Z. Omar
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Second Order ◽  
Direct Solution ◽  
Block Method ◽  
One Step ◽  
Third Derivative ◽  
Two Hybrid

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.

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.

scholarly journals Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Mohammad Alkasassbeh ◽  
Zurni Omar
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Initial Value Problems ◽  
Second Order ◽  
Block Method ◽  
Initial Value ◽  
One Step ◽  
Approximate Function ◽  
The Given ◽  
Third Derivative

A new one-step block method with generalized three hybrid points for solving initial value problems of second-order ordinary differential equations directly is proposed. In deriving this method, a power series approximate function is interpolated at {xn,xn+r} while its second and third derivatives are collocated at all points {xn,xn+r,xn+s,xn+t,xn+1} in the given interval. The proposed method is then tested on initial value problems of second-order ordinary differential equations solved by other methods previously. The numerical results confirm the superiority of the new method to the existing methods in terms of accuracy.

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

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