Unification of the Bernstein-type polynomials and their applications

Boundary value problems

Yilmaz Simsek¹ 

[1] Department of Mathematics, Faculty of Science, University of Akdeniz, Antalya, Turkey

关键词: Bernstein polynomials;    generating function;    Bezier curves;    Laplace transform;    functional equation;    high-order differential equations;    Bernstein-Galerkin method;    Bernoulli polynomials;    Bernoulli numbers;    Euler polynomials;    Euler numbers;    Genocchi polynomials;    Genocchi numbers;    Stirling numbers of the second kind;   

DOI  :  10.1186/1687-2770-2013-56

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we investigate some new identities related to the unification of the Bernstein-type polynomials, Bernoulli polynomials, Euler numbers and Stirling numbers of the second kind. We also give some remarks and applications of the Bernstein-type polynomials related to solving high even-order differential equations by using the Bernstein-Galerkin method. We also give some applications on these polynomials and differential equations. MSC:11B68, 12D10, 14F10, 26C05, 26C10, 30B40, 30C15, 42A38, 44A10.

【 授权许可】

CC BY