ISSN 1119-4618
 

Original Research 


Multivalue multistep implicit second derivative methods for the numerical integration of stiff ordinary differential equations

Dauda Gulibur Yakubu, Mohammed Abdulhameed, Garba Tahiru Adamu, Isah Abdullahi.

Abstract
In this paper, we introduce multivalue multistep implicit methods with second derivative evaluations for continuous solution of stiff systems. The proposed methods are derived by introducing intermediate off-step points in between the familiar step-points suitable for continuous solution of stiff systems. Considerable gain in efficiency, accuracy and stability are achieved by the modification of the methods to contain second derivative evaluations. Plots of the stability regions in the complex plane show that they are stable, convergent, with large regions of absolute stability. A global error estimation of the approximate solution is described. The new methods show remarkable performance over a broad class of linear and nonlinear stiff systems, due to their high order of accuracy and stiffly accurate characteristic properties. The results of preliminary experiments are presented which are in better agreement with the exact solutions.

Key words: Block method, Continuous scheme, Multistep method, Second derivative method, Stiff system


 
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How to Cite this Article
Pubmed Style

Yakubu DG, Abdulhameed M, Adamu GT, Abdullahi I. Multivalue multistep implicit second derivative methods for the numerical integration of stiff ordinary differential equations. JPAS. 2022; 22(1): 43-55. doi:10.5455/sf.amohd


Web Style

Yakubu DG, Abdulhameed M, Adamu GT, Abdullahi I. Multivalue multistep implicit second derivative methods for the numerical integration of stiff ordinary differential equations. https://www.atbuscienceforum.com/?mno=84926 [Access: November 12, 2022]. doi:10.5455/sf.amohd


AMA (American Medical Association) Style

Yakubu DG, Abdulhameed M, Adamu GT, Abdullahi I. Multivalue multistep implicit second derivative methods for the numerical integration of stiff ordinary differential equations. JPAS. 2022; 22(1): 43-55. doi:10.5455/sf.amohd



Vancouver/ICMJE Style

Yakubu DG, Abdulhameed M, Adamu GT, Abdullahi I. Multivalue multistep implicit second derivative methods for the numerical integration of stiff ordinary differential equations. JPAS. (2022), [cited November 12, 2022]; 22(1): 43-55. doi:10.5455/sf.amohd



Harvard Style

Yakubu, D. G., Abdulhameed, . M., Adamu, . G. T. & Abdullahi, . I. (2022) Multivalue multistep implicit second derivative methods for the numerical integration of stiff ordinary differential equations. JPAS, 22 (1), 43-55. doi:10.5455/sf.amohd



Turabian Style

Yakubu, Dauda Gulibur, Mohammed Abdulhameed, Garba Tahiru Adamu, and Isah Abdullahi. 2022. Multivalue multistep implicit second derivative methods for the numerical integration of stiff ordinary differential equations. Science Forum (Journal of Pure and Applied Sciences), 22 (1), 43-55. doi:10.5455/sf.amohd



Chicago Style

Yakubu, Dauda Gulibur, Mohammed Abdulhameed, Garba Tahiru Adamu, and Isah Abdullahi. "Multivalue multistep implicit second derivative methods for the numerical integration of stiff ordinary differential equations." Science Forum (Journal of Pure and Applied Sciences) 22 (2022), 43-55. doi:10.5455/sf.amohd



MLA (The Modern Language Association) Style

Yakubu, Dauda Gulibur, Mohammed Abdulhameed, Garba Tahiru Adamu, and Isah Abdullahi. "Multivalue multistep implicit second derivative methods for the numerical integration of stiff ordinary differential equations." Science Forum (Journal of Pure and Applied Sciences) 22.1 (2022), 43-55. Print. doi:10.5455/sf.amohd



APA (American Psychological Association) Style

Yakubu, D. G., Abdulhameed, . M., Adamu, . G. T. & Abdullahi, . I. (2022) Multivalue multistep implicit second derivative methods for the numerical integration of stiff ordinary differential equations. Science Forum (Journal of Pure and Applied Sciences), 22 (1), 43-55. doi:10.5455/sf.amohd