Version 1
: Received: 15 April 2022 / Approved: 18 April 2022 / Online: 18 April 2022 (08:28:47 CEST)
How to cite:
Otegbeye, O.; Oloniiju, S.; Marewo, G. A Modified Piecewise Relaxation Method for Singular Initial Value Problems. Preprints2022, 2022040159. https://doi.org/10.20944/preprints202204.0159.v1
Otegbeye, O.; Oloniiju, S.; Marewo, G. A Modified Piecewise Relaxation Method for Singular Initial Value Problems. Preprints 2022, 2022040159. https://doi.org/10.20944/preprints202204.0159.v1
Otegbeye, O.; Oloniiju, S.; Marewo, G. A Modified Piecewise Relaxation Method for Singular Initial Value Problems. Preprints2022, 2022040159. https://doi.org/10.20944/preprints202204.0159.v1
APA Style
Otegbeye, O., Oloniiju, S., & Marewo, G. (2022). A Modified Piecewise Relaxation Method for Singular Initial Value Problems. Preprints. https://doi.org/10.20944/preprints202204.0159.v1
Chicago/Turabian Style
Otegbeye, O., Shina Oloniiju and Gerald Marewo. 2022 "A Modified Piecewise Relaxation Method for Singular Initial Value Problems" Preprints. https://doi.org/10.20944/preprints202204.0159.v1
Abstract
In gravitational theory and astrophysical dynamics, singular initial value problems (IVPs) are frequently encountered. Finding the solutions to this class of IVPs can be challenging due to their complex nature. This study strives to circumvent the complexity by proposing a numerical method for solving such problems. The approach proposed in the current research seeks solutions to the IVP by partitioning the domain [0,L] of the problem into two intervals and solving the problem on each domain. The study seeks a closed-form solution to the IVP in the interval containing the singular point. A linearization technique and piecewise partitioning of the domain not containing the singularity are applied to the nonlinear IVP. The resulting linearized differential equation is solved using the Chebyshev spectral collocation method. Some examples are presented to illustrate the efficiency of the proposed method. Numerical analysis of the solution and residual errors are shown to ascertain convergence and accuracy. The results suggest that the technique gives accurate convergent solutions using a few collocation points.
Keywords
relaxation; spectral methods; multi-domain
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
