A New Nonlinear Hybrid Technique with fixed and adaptive step-size approaches

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Sigma Mühendislik ve Fen Bilimleri Dergisi
Volume:40 Issue:1
A New Nonlinear Hybrid Technique with fixed and adaptive step-size approaches

A New Nonlinear Hybrid Technique with fixed and adaptive step-size approaches

Authors : Amanullah SOOMRO, Sania QURESHI, Asif Ali SHAIKH

Pages : 162-178

View : 25 | Download : 8

Publication Date : 2022-03-25

Article Type : Research Paper

Abstract :Linear and nonlinear numerical techniques are the most popular techniques for finding approximate solutions to initial value problems in numerous scientific fields. Due to the substantial importance of ordinary differential equations, an attempt has been made in the present research study to obtain a new nonlinear hybrid technique based upon contra-harmonic and harmonic means having fourth-order accuracy. Theoretical analysis in terms of consistency, stability, asymptotic errors insert ignore into journalissuearticles values(local and global truncation errors);, and convergence has also been carried out. The newly formulated technique is compared with some existing techniques having the same characteristics and observed to be much better because of errors, CPU time, and stability region. The adaptive step-size approach improves the performance of the proposed technique, and strategies to control the errors are developed. Some numerical experiments for scalar and vector initial value problems, including logistic growth, sinusoidal and industrial Robot Arm systems, are presented to show better performance of the proposed technique.
Keywords : Local error, Global error, Stability, Convergence, Asymptotic error, Variable step size

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