Approximate Solutions of Differential Equations by Using the Bernstein Polynomials | Zendy

Yadollah Ordokhani | Zendy; S. Davaei far | Zendy

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Approximate Solutions of Differential Equations by Using the Bernstein Polynomials

Author(s) -

Yadollah Ordokhani,

S. Davaei far

Publication year - 2011

Publication title -

isrn applied mathematics

Language(s) - English

Resource type - Journals

eISSN - 2090-5572

pISSN - 2090-5564

DOI - 10.5402/2011/787694

Subject(s) - bernstein polynomial , mathematics , legendre polynomials , differential equation , algebraic equation , polynomial , mathematical analysis , recurrence relation , relation (database) , classical orthogonal polynomials , orthogonal polynomials , nonlinear system , computer science , physics , quantum mechanics , database

A numerical method for solving differential equations by approximating the solution in the Bernstein polynomial basis is proposed. At first, we demonstrate the relation between the Bernstein and Legendre polynomials. By using this relation, we derive the operational matrices of integration and product of the Bernstein polynomials. Then, we employ them for solving differential equations. The method converts the differential equation to a system of linear algebraic equations. Finallysome examples and their numerical solutions are given; comparing the results with the numerical resultsobtained from the other methods, we show the high accuracy and efficiency of the proposed method.

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