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Solving systems of algebraic equations

100%

Kiciak P.

Machine Graphics and Vision

2002

tom Vol. 11, No. 4

455-473

Numerical procedutes of solving a system for algebraic equations usually consist of a part that localizes the solutions and a part that computers their accurate approximations. The localization is often based on the convex hull property of the Bernstein-Bezier representation of the equations. In the procedure described in this paper, the convex hull test is complemented with another, which significantly improves the efficiency of the procedures.

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

100%

Sriwastav N. , Barnwal A. K. , Wazwaz A.-M. , Singh M.

Opuscula Mathematica

2023

tom Vol. 43, no. 4

575--601

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.

Inverse theorem in simultaneous approximation by Micchelli combination of Bernstein polynomials

86%

Agrawal P.

Demonstratio Mathematica

1998

tom Vol. 31, nr 1

55-62

The present paper is a continuation of our work [1]. Here we have studied the inverse theorem

A new approach for solving Bratu’s problem

72%

Ghomanjani F. , Shateyi S.

Demonstratio Mathematica

2019

tom Vol. 52, nr 1

336--346

A numerical technique for one-dimensional Bratu’s problem is displayed in this work. The technique depends on Bernstein polynomial approximation. Numerical examples are exhibited to verify the efficiency and accuracy of the proposed technique. In this sequel, the obtained error was shown between the proposed technique, Chebyshev wavelets, and Legendre wavelets. The results display that this technique is accurate.