TY  - JOUR
T1  - An A-Stable Uniformly Order Seven Block Hybrid Method for Solving Nonlinear Initial Value Problems
AU  - Taiye, Oyedepo
AU  - Akanbi, Bello Kareem
AU  - Abdullahi, Ayinde Muhammed
AU  - Adenipekun, Adewale Emmanuel
PY  - 2025
DA  - November
Y2  - 2025
JF  - Cankaya University Journal of Science and Engineering
JO  - CUJSE
PB  - Cankaya University
WT  - DergiPark
SN  - 2564-7954
SP  - 63
EP  - 72
VL  - 22
IS  - 2
LA  - en
AB  - This study presents the development of a new A-stable uniformly order seven block hybrid method for solving Nonlinear Initial Value Problems (NIVPs) in Ordinary Differential Equations (ODEs). Traditional numerical methods, including Euler’s method and Runge-Kutta methods, often struggle with nonlinear problems due to stability and computational inefficiencies, especially when dealing with stiff equations. To address this limitation, the proposed method integrates the advantages of block hybrid techniques, ensuring A-stability and uniform order seven, which enhances both accuracy and computational efficiency. The formulation of the method involves applying a one-step linear multistep approach combined with interpolation and collocation techniques. Through extensive analysis, the method is shown to satisfy essential numerical properties such as consistency, zero-stability, and convergence. Numerical experiments demonstrate that the new method outperforms existing methods in terms of accuracy and computational cost, particularly for stiff nonlinear problems. The method’s performance is validated by applying it to various test cases, yielding results consistent with previous studies and showing significant improvements in error reduction.
KW  - A-stable
KW  - Block Hybrid 
Method
KW  - Nonlinear Initial 
Value Problems
KW  - Numerical Methods
KW  - Stiffness
KW  - Accuracy
KW  - Computational 
Efficiency
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UR  - https://dergipark.org.tr/en/pub/cankujse/article/1706554
L1  - https://dergipark.org.tr/en/download/article-file/4902860
ER  -