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Falkner Type Hybrid Block Method for Solving Second-order IVPs in ODEs

This study uses Falkner-type hybrid block methods to address the numerical solution of second-order ordinary differential equations (ODEs). The primary challenge with traditional approaches is their limited efficiency and accuracy in handling stiff ODEs and complex boundary conditions. A novel hybrid block method that integrates the Falkner framework with fixed step-size techniques is proposed to overcome these limitations. The coefficients of the new schemes are obtained via Taylor’s series expansion. The transformation of the derived methods to the block scheme promotes easy implementation and enhances convergence. The hybrid scheme is implemented, and its performance is validated through a series of benchmark problems, comparing the numerical solution of the proposed scheme with the exact solution of ODEs problems. The efficacy of this method is demonstrated with two numerical experiments, elucidating its stability and convergence properties. The results show the computational efficacy of the new scheme, which shows that the proposed scheme is a novel numerical tool for solving second-order ODEs with implications for various application areas in engineering and applied mathematics.

Author(s)
R. I. OKUONGHAE
I. B. AIHIE
Volume
2
Keyword(s)
Falkner hybrid method, hybrid block method,
dose rate.
stiff problems
oscillatory problems
second-order initial value problems
Year
2025
Page Number
17-27
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BJPS 2(1) Paper 2.pdf (709.67 KB)
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