TY - JOUR
T1 - BERNSTEIN OPERATIONAL MATRIX OF DIFFERENTIATION AND COLLOCATION APPROACH FOR A CLASS OF THREE-POINT SINGULAR BVPS
T2 - ERROR ESTIMATE AND CONVERGENCE ANALYSIS
AU - Sriwastav, Nikhil
AU - Barnwal, Amit K.
AU - Wazwaz, Abdul Majid
AU - Singh, Mehakpreet
N1 - Publisher Copyright:
© 2023 Authors. Creative Commons CC-BY 4.0.
PY - 2023
Y1 - 2023
N2 - 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.
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 - convergence analysis
KW - error estimate
KW - three-point singular BVPs
UR - http://www.scopus.com/inward/record.url?scp=85162861724&partnerID=8YFLogxK
U2 - 10.7494/OpMath.2023.43.4.575
DO - 10.7494/OpMath.2023.43.4.575
M3 - Article
AN - SCOPUS:85162861724
SN - 1232-9274
VL - 43
SP - 575
EP - 601
JO - Opuscula Mathematica
JF - Opuscula Mathematica
IS - 4
ER -