Home|Journals|Articles by Year|Audio Abstracts
 

Original Research

JPAS. 2022; 22(1): 43-55


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






Full-text options


Share this Article


Online Article Submission
• ejmanager.com




ejPort - eJManager.com
Refer & Earn
JournalList
About BiblioMed
License Information
Terms & Conditions
Privacy Policy
Contact Us

The articles in Bibliomed are open access articles licensed under Creative Commons Attribution 4.0 International License (CC BY), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.