scholarly journals AN IMPLICIT ONE-STEP THIRD DERIVATIVE HYBRID BLOCK METHOD FOR THE NUMERICAL SOLUTION OF FIRST ORDER INITIAL VALUE PROBLEMS IN ORDINARY DIFFERENTIAL EQUATIONS.

IARJSET ◽  
2021 ◽  
Vol 8 (8) ◽  
Author(s):  
Ononogbo , .C. B. ◽  
Julia , .U. E. ◽  
Ishie, .I.H.
Author(s):  
J. Sabo ◽  
T. Y. Kyagya ◽  
M. Solomon

In this research, we have proposed the simulation of linear block algorithm for modeling third order highly stiff problem without reduction to a system of first order ordinary differential equation, to address the weaknesses in reduction method. The method is derived using the linear block method through interpolation and collocation. The basic properties of the block method were recovered and was found to be consistent, convergent and zero-stability. The new block method is been applied to model third order initial value problems of ordinary differential equations without reducing the equations to their equivalent systems of first order ordinary differential equations. The result obtained on the process on some sampled modeled third order linear problems give better approximation than the existing methods which we compared our result with.


2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Mohammad Alkasassbeh ◽  
Zurni Omar

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.


Author(s):  
Y. Skwame ◽  
J. Sabo ◽  
M. Mathew

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.


OALib ◽  
2018 ◽  
Vol 05 (07) ◽  
pp. 1-15
Author(s):  
Toyin Gideon Okedayo ◽  
Ayodele Olakiitan Owolanke ◽  
Olaseni Taiwo Amumeji ◽  
Muyiwa Philip Adesuyi

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