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

Amanullah Soomro; Sania Qureshı; Asif Ali Shaıkh

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

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 (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

References

The article references can be accessed from the .pdf file.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Amanullah Soomro This is me
0000-0002-7225-2309
Pakistan

Sania Qureshı ^* This is me
0000-0002-5823-0170
Türkiye

Asif Ali Shaıkh This is me
0000-0002-3084-922X
Pakistan

Publication Date

March 25, 2022

Submission Date

August 25, 2021

Acceptance Date

October 4, 2021

Published in Issue

Year 2022 Volume: 40 Number: 1

IZ

https://izlik.org/JA66EK45CB

Cite

RIS / Bibtex

APA

Soomro, A., Qureshı, S., & Shaıkh, A. A. (2022). A New Nonlinear Hybrid Technique with fixed and adaptive step-size approaches. Sigma Journal of Engineering and Natural Sciences, 40(1), 162-178. https://izlik.org/JA66EK45CB

AMA

1.Soomro A, Qureshı S, Shaıkh AA. A New Nonlinear Hybrid Technique with fixed and adaptive step-size approaches. SIGMA. 2022;40(1):162-178. https://izlik.org/JA66EK45CB

Chicago

Soomro, Amanullah, Sania Qureshı, and Asif Ali Shaıkh. 2022. “A New Nonlinear Hybrid Technique With Fixed and Adaptive Step-Size Approaches”. Sigma Journal of Engineering and Natural Sciences 40 (1): 162-78. https://izlik.org/JA66EK45CB.

EndNote

Soomro A, Qureshı S, Shaıkh AA (March 1, 2022) A New Nonlinear Hybrid Technique with fixed and adaptive step-size approaches. Sigma Journal of Engineering and Natural Sciences 40 1 162–178.

IEEE

[1]A. Soomro, S. Qureshı, and A. A. Shaıkh, “A New Nonlinear Hybrid Technique with fixed and adaptive step-size approaches”, SIGMA, vol. 40, no. 1, pp. 162–178, Mar. 2022, [Online]. Available: https://izlik.org/JA66EK45CB

ISNAD

Soomro, Amanullah - Qureshı, Sania - Shaıkh, Asif Ali. “A New Nonlinear Hybrid Technique With Fixed and Adaptive Step-Size Approaches”. Sigma Journal of Engineering and Natural Sciences 40/1 (March 1, 2022): 162-178. https://izlik.org/JA66EK45CB.

JAMA

1.Soomro A, Qureshı S, Shaıkh AA. A New Nonlinear Hybrid Technique with fixed and adaptive step-size approaches. SIGMA. 2022;40:162–178.

MLA

Soomro, Amanullah, et al. “A New Nonlinear Hybrid Technique With Fixed and Adaptive Step-Size Approaches”. Sigma Journal of Engineering and Natural Sciences, vol. 40, no. 1, Mar. 2022, pp. 162-78, https://izlik.org/JA66EK45CB.

Vancouver

1.Amanullah Soomro, Sania Qureshı, Asif Ali Shaıkh. A New Nonlinear Hybrid Technique with fixed and adaptive step-size approaches. SIGMA [Internet]. 2022 Mar. 1;40(1):162-78. Available from: https://izlik.org/JA66EK45CB