Trigonometric-Fitted One-Step 3 Points Hybrid Block Method for the Solution of Stiff and Oscillating Problems
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Page Numbers:
461-471
Digital Object Identifier:
10.58578/amjsai.v1i1.3551
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Authors:
Raymond Dominic1, Adedokun Opeyemi Benjamin2, Olanrewaju Philip Oladapo3 
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Authors retain copyright and grant the journal right of first publication.
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Abstract
This paper introduces a novel Trigonometric-Fitted One-Step 3 Points Hybrid Block Method tailored for addressing the complexities associated with stiff and oscillating differential equations.The continuous hybrid technique was created using the interpolation method and the collocation of the trigonometrical function as the basis function. It was then eval_uated at non-interpolating points by inculcating the transformation method to produce a continuous block method. When the continuous block was assessed at each stage, the discrete block approach was regained. Upon investigation, the fundamental characteristics of the techniques were discovered to be zero-stable, consistent, and convergent. The new method is used to solve a few stiff and oscillatory ordinary differential equation problems. Comparisons of numerical results of the derived methods, it was found that our approach provides a better approximation than the existing method cited in the reference.
AMS subject classification: 65L05, 65L06, 65L20
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References
[2] Abdulganiy, R. I., Akinfenwa, O. A. & Okunuga, S. A. (2021). Block Trigonometrically Fitted Block Backward Differentiation formula for the Initial Value Problem with Oscillating Solutions. Nigerian Journal of Basic and Applied Science, 29(1): 01-12. DOI: http://dx.doi.org/10.4314/njbas.v29i1.1
[3]Adeneran, A. O., & Olanegan, O.O., (2019). Two step Trigonometrically Fitted Method for Numerical Solution of the Initial Value Problem with Oscillating Solutions. Journal of Advances in Mathematics and Computer Science, 30(3): 1-7.
[4]Abdulganiy, R. I. (2018). Trigonometrically Fitted Block Backward Differentiation Methods for First Order Initial Value Problems with Periodic Solution. Journal of Advances in Mathematics and Computer Science, 28(5): 1-14.
[5]Abdulganiy, R. I., Akinfenwa, O. A. & Okunuga, S. A. (2017). Maximal Order Block Trigonometrically Fitted Scheme for the Numerical Treatment of Second Order Initial Value Problem with Oscillating Solutions. International Journal of Mathematical Analysis and Optimization, 2017: 168-186
[6]Abdulganiy, R. I., Akinfenwa, O. A. & Okunuga, S. A. (2018). Construction of L Stable Second Derivative Trigonometrically Fitted Block Backward Differentiation Formula for the Solution of Oscillatory Initial Value Problems. African Journal of Science, Technology, Innovation and Development, 10(4): 411-419.
[7]Jator, S. N., Swindell, S., and French, R. D. (2013). Trigonmetrically Fitted Block Numerov Type Method for ( ). Numer Algor, 62: 13-26
[8] Ngwane, F. F. & Jator, S. N. (2014). Trigonometrically-Fitted Second Derivative Method for Oscillatory Problems. Springer Plus, 3:304.
[9] Ngwane, F. F. & Jator, S. N. (2015). A Family of Trigonometrically Fitted Enright Second Derivative Methods for Stiff and Oscillatory Initial Value problems. Journal of Applied Mathematics. 2015, 1-17.
[10] Ngwane, F.F. & Jator, S.N. (2013b). Block hybrid method using trigonometric basis for initial problems with oscillating solutions. Numerical Algorithm, 63: 713-725.
[11] Adeniran A.O., Edaogbogun K. (2021) Half Step Numerical Method for Solution of Second orderinitial value problems. Academic Journal of Applied Mathematical Sciences,Vol. 7, Issue. 2, pp: 77-81,
[12] Kayode, S.J., & Obarhua, F. O (2015) 3-Step y-function hybrid methods for direct numerical integration of second order IVPs. Theoritical Mathematics & Applications,Vol. 5, Issue. 1, pp: 39-51,