TY  - JOUR
ID  - Sriwastav2023
LB  - Sriwastav2023
AU  - Sriwastav, Nikhil
AU  - Barnwal, Amit K.
AU  - Wazwaz, Abdul-Majid
AU  - Singh, Mehakpreet
TI  - Bernstein operational matrix of differentiation and collocation approach for a class of three-point singular BVPs: error estimate and convergence analysis
ST  - Bernstein operational matrix of differentiation and collocation approach for a class of three-point singular BVPs: error estimate and convergence analysis
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2023
VL  - 43
IS  - 4
SP  - 575
EP  - 601
DO  - https://doi.org/10.7494/OpMath.2023.43.4.575
UR  - https://doi.org/10.7494/OpMath.2023.43.4.575
AB  - 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.
KW  - Bernstein polynomials
KW  - collocation method
KW  - three-point singular BVPs
KW  - convergence analysis
KW  - error estimate
SN  - 1232-9274
ER  -