Collocation Technique Based on Chebyshev Polynomials to Solve Emden–Fowler-Type Singular Boundary Value Problems with Derivative Dependence

Shabanam Kumari, Arvind Kumar Singh () and Utsav Gupta
Additional contact information
Shabanam Kumari: Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
Arvind Kumar Singh: Department of Mathematics, Institute of Science, Banaras Hindu University, Varanasi 221005, India
Utsav Gupta: Tanglin Trust School, 95 Portsdown Rd, Singapore 139299, Singapore

Mathematics, 2024, vol. 12, issue 4, 1-16

Abstract: In this work, an innovative technique is presented to solve Emden–Fowler-type singular boundary value problems (SBVPs) with derivative dependence. These types of problems have significant applications in applied mathematics and astrophysics. Initially, the differential equation is transformed into a Fredholm integral equation, which is then converted into a system of nonlinear equations using the collocation technique based on Chebyshev polynomials. Subsequently, an iterative numerical approach, such as Newton’s method, is employed on the system of nonlinear equations to obtain an approximate solution. Error analysis is included to assess the accuracy of the obtained solutions and provide insights into the reliability of the numerical results. Furthermore, we graphically compare the residual errors of the current method to the previously established method for various examples.

Keywords: Chebyshev polynomials; Emden–Fowler-type SBVPs; derivative dependence; functional approximation; Green’s function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/4/592/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/4/592/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:4:p:592-:d:1340316

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().