A Block Trigonometrically Fitted Backward Differentiation Formula for the Numerical Solution of Initial Value Problem with Oscillating Solutions

R. I. Abdulganiy; O. A. Akinfenwa and S. A. Okunuga

doi:10.4314/njbas.v29i1.1

E-ISSN 2756-4843 | ISSN 0794-5698

2022, Vol: 30, Issue: 1

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Original Research

Nig. J. Basic Appl. Sci.. 2021; 29(1): 1-12

doi: 10.4314/njbas.v29i1.1

A Block Trigonometrically Fitted Backward Differentiation Formula for the Numerical Solution of Initial Value Problem with Oscillating Solutions

R. I. Abdulganiy, O. A. Akinfenwa and S. A. Okunuga.

Abstract
A block trigonometrically fitted backward differentiation formula (BTBDF) whose coefficients are functions of frequency and step size especially designed for the solution of first order initial value problems (IVPs) with oscillatory solution is proposed in this paper. The BTBDF is obtained from three discrete formulas which are provided by continuous second derivative trigonometrically fitted method (CSDTFM). The BTBDF is implemented in a block by block fashion which makes it self-starting method. The convergence of the BTBDF is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy advantage

Key words: Backward Differentiation Formula, Collocation, Continuous Form, Convergence

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Pubmed Style

Abdulganiy RI, . A Block Trigonometrically Fitted Backward Differentiation Formula for the Numerical Solution of Initial Value Problem with Oscillating Solutions. Nig. J. Basic Appl. Sci.. 2021; 29(1): 1-12. doi:10.4314/njbas.v29i1.1

Web Style

Abdulganiy RI, . A Block Trigonometrically Fitted Backward Differentiation Formula for the Numerical Solution of Initial Value Problem with Oscillating Solutions. https://www.njbas-udus.com/?mno=271523 [Access: July 22, 2022]. doi:10.4314/njbas.v29i1.1

AMA (American Medical Association) Style

Abdulganiy RI, . A Block Trigonometrically Fitted Backward Differentiation Formula for the Numerical Solution of Initial Value Problem with Oscillating Solutions. Nig. J. Basic Appl. Sci.. 2021; 29(1): 1-12. doi:10.4314/njbas.v29i1.1

Vancouver/ICMJE Style

Abdulganiy RI, . A Block Trigonometrically Fitted Backward Differentiation Formula for the Numerical Solution of Initial Value Problem with Oscillating Solutions. Nig. J. Basic Appl. Sci.. (2021), [cited July 22, 2022]; 29(1): 1-12. doi:10.4314/njbas.v29i1.1

Harvard Style

Abdulganiy, R. I. & (2021) A Block Trigonometrically Fitted Backward Differentiation Formula for the Numerical Solution of Initial Value Problem with Oscillating Solutions. Nig. J. Basic Appl. Sci., 29 (1), 1-12. doi:10.4314/njbas.v29i1.1

Turabian Style

Abdulganiy, R. I., and O. A. Akinfenwa and S. A. Okunuga. 2021. A Block Trigonometrically Fitted Backward Differentiation Formula for the Numerical Solution of Initial Value Problem with Oscillating Solutions. Nigerian Journal of Basic and Applied Sciences, 29 (1), 1-12. doi:10.4314/njbas.v29i1.1

Chicago Style

Abdulganiy, R. I., and O. A. Akinfenwa and S. A. Okunuga. "A Block Trigonometrically Fitted Backward Differentiation Formula for the Numerical Solution of Initial Value Problem with Oscillating Solutions." Nigerian Journal of Basic and Applied Sciences 29 (2021), 1-12. doi:10.4314/njbas.v29i1.1

MLA (The Modern Language Association) Style

APA (American Psychological Association) Style

Abdulganiy, R. I. & (2021) A Block Trigonometrically Fitted Backward Differentiation Formula for the Numerical Solution of Initial Value Problem with Oscillating Solutions. Nigerian Journal of Basic and Applied Sciences, 29 (1), 1-12. doi:10.4314/njbas.v29i1.1

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