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Approximate Solutions of Differential Equations by Using the Bernstein Polynomials
Joint Authors
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-15, 15 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-06-20
Country of Publication
Egypt
No. of Pages
15
Main Subjects
Abstract EN
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.
Finally some examples and their numerical solutions are given; comparing the results with the numerical results obtained from the other methods, we show the high accuracy and efficiency of the proposed method.
American Psychological Association (APA)
Ordokhani, Y.& Davaei far, S.. 2011. Approximate Solutions of Differential Equations by Using the Bernstein Polynomials. ISRN Applied Mathematics،Vol. 2011, no. 2011, pp.1-15.
https://search.emarefa.net/detail/BIM-498118
Modern Language Association (MLA)
Ordokhani, Y.& Davaei far, S.. Approximate Solutions of Differential Equations by Using the Bernstein Polynomials. ISRN Applied Mathematics No. 2011 (2011), pp.1-15.
https://search.emarefa.net/detail/BIM-498118
American Medical Association (AMA)
Ordokhani, Y.& Davaei far, S.. Approximate Solutions of Differential Equations by Using the Bernstein Polynomials. ISRN Applied Mathematics. 2011. Vol. 2011, no. 2011, pp.1-15.
https://search.emarefa.net/detail/BIM-498118
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-498118