Bernstein operational matrix of differentiation and collocation approach for a class of three-point singular BVPs: error estimate and convergence analysis

• Autorzy: Sriwastav Nikhil , Barnwal Amit K. , Wazwaz Abdul-Majid , Singh Mehakpreet

Identyfikatory

DOI

10.7494/OpMath.2023.43.4.575

• Języki publikacji: EN

Abstrakty

EN

Singular boundary value problems (BVPs) have widespread applications in the field of engineering, chemical science, astrophysics and mathematical biology. Finding an approximate solution to a problem with both singularity and non-linearity is highly challenging. The goal of the current study is to establish a numerical approach for dealing with problems involving three-point boundary conditions. The Bernstein polynomials and collocation nodes of a domain are used for developing the proposed numerical approach. The straightforward mathematical formulation and easy to code, makes the proposed numerical method accessible and adaptable for the researchers working in the field of engineering and sciences. The priori error estimate and convergence analysis are carried out to affirm the viability of the proposed method. Various examples are considered and worked out in order to illustrate its applicability and effectiveness. The results demonstrate excellent accuracy and efficiency compared to the other existing methods.

Słowa kluczowe

EN

Bernstein polynomials; collocation method; three-point singular BVPs; convergence analysis; error estimate

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2023
• Tom: Vol. 43, no. 4
• Strony: 575--601
• Opis fizyczny: Bibliogr. 53 poz., rys., tab., wykr.

Twórcy

autor

Sriwastav Nikhil

• Madan Mohan Malaviya University of Technology, Department of Mathematics and Scientific Computing, Gorakhpur – 273010, India

• https://orcid.org/0000-0002-1667-2122

autor

Barnwal Amit K.

• Madan Mohan Malaviya University of Technology, Department of Mathematics and Scientific Computing, Gorakhpur – 273010, India

• https://orcid.org/0000-0003-3615-7723

autor

Wazwaz Abdul-Majid

• Saint Xavier University, Department of Mathematics, Chicago, IL 60655, USA

• https://orcid.org/0000-0002-8325-7500

autor

Singh Mehakpreet

• University of Limerick, Department of Mathematics and Statistics, V94 T9PX Limerick, Ireland

• https://orcid.org/0000-0002-6392-6068

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Uwagi

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)