Research Article
A Sixth-order Hybrid Block Method for the Direct Solution of 3rd-order Initial Value Problems of Ordinary Differential Equations
Issue:
Volume 10, Issue 2, December 2026
Pages:
24-35
Received:
7 June 2026
Accepted:
22 June 2026
Published:
17 July 2026
DOI:
10.11648/j.engmath.20261002.11
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Views:
Abstract: This work focuses on the derivation, analysis and numerical application of a hybrid linear multistep formula for directly solving third-order initial value problems (IVPs) ordinary differential equations (ODEs). The method is derived by adopting the collocation and interpolation procedure with a power series polynomial of degree eight as the basis function. The procedure resulted in the construction of a continuous hybrid linear multistep method by collocating the third derivative at nodal and five off-nodal points to generate a system of linear equations for the determination of the unknown parameters, from which the formulas that constitute the proposed hybrid block method are obtained. The suggested method is fully hybrid, which is an important property that contributed to the good accuracy and minimum errors associated with the results of the method. The analysis of the basic properties of the suggested method reveals that the method is of theoretical order six, stable, consistent and convergent. Four numerical examples are considered for the numerical experiment to confirm the accuracy of the proposed method. The experiment shows that the present method is very efficient for the numerical approximation of third-order initial value problems for ordinary differential equations. The method also performs favorably well when compared with the results of some cited methods in the literature.
Abstract: This work focuses on the derivation, analysis and numerical application of a hybrid linear multistep formula for directly solving third-order initial value problems (IVPs) ordinary differential equations (ODEs). The method is derived by adopting the collocation and interpolation procedure with a power series polynomial of degree eight as the basis ...
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Akinmoladun Olusegun Mayowa
