Open AccessAccurate Numerical Method for Singular Initial-Value Problems
Author(s) -
Tesfaye Aga Bullo,
Gemechis File Duressa,
Gashu Gadisa Kiltu
Publication year - 2021
Publication title -
advanced computational intelligence : an international journal
Language(s) - English
Resource type - Journals
ISSN - 2454-3934
DOI - 10.5121/acii.2021.8301
Subject(s) - runge–kutta methods , initial value problem , convergence (economics) , mathematics , numerical analysis , singular solution , stability (learning theory) , value (mathematics) , order (exchange) , singular value , mathematical analysis , mathematical optimization , computer science , physics , statistics , eigenvalues and eigenvectors , finance , quantum mechanics , machine learning , economics , economic growth
In this paper, an accurate numerical method is presented to find the numerical solution of the singular initial value problems. The second-order singular initial value problem under consideration is transferred into a first-order system of initial value problems, and then it can be solved by using the fifth-order Runge Kutta method. The stability and convergence analysis is studied. The effectiveness of the proposed methods is confirmed by solving three model examples, and the obtained approximate solutions are compared with the existing methods in the literature. Thus, the fifth-order Runge-Kutta method is an accurate numerical method for solving the singular initial value problems.