Bernstein polynomials method for numerical solutions of integro-differential form of the singular Emden-Fowler initial value problems
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Authors
Abdelkrim Bencheikh
- Department of Mathematics, University Kasdi-Merbah, Ouargla, 30000, Algeria.
Lakhdar Chiter
- Department of Mathematics, Ferhat-Abbas University, Setif, 19000, Algeria.
Hocine Abbassi
- Department of Mathematics, University Kasdi-Merbah, Ouargla, 30000, Algeria.
Abstract
In this paper, Bernstein polynomial method applied to the solutions of generalized Emden-Fowler equations as singular
initial value problems is presented. Firstly, the singular differential equations are converted to Volterra integro-differential
equations and then solved by the Bernstein polynomials method. The properties of Bernstein polynomials via Gauss-Legendre
rule are used to reduce the integral equations to a system of algebraic equations which can be solved numerically. Some
illustrative examples are discussed to demonstrate the validity and applicability of the present method.
Share and Cite
ISRP Style
Abdelkrim Bencheikh, Lakhdar Chiter, Hocine Abbassi, Bernstein polynomials method for numerical solutions of integro-differential form of the singular Emden-Fowler initial value problems, Journal of Mathematics and Computer Science, 17 (2017), no. 1, 66-75
AMA Style
Bencheikh Abdelkrim, Chiter Lakhdar, Abbassi Hocine, Bernstein polynomials method for numerical solutions of integro-differential form of the singular Emden-Fowler initial value problems. J Math Comput SCI-JM. (2017); 17(1):66-75
Chicago/Turabian Style
Bencheikh, Abdelkrim, Chiter, Lakhdar, Abbassi, Hocine. "Bernstein polynomials method for numerical solutions of integro-differential form of the singular Emden-Fowler initial value problems." Journal of Mathematics and Computer Science, 17, no. 1 (2017): 66-75
Keywords
- Bernstein polynomials
- Volterra integro-differential equations
- Emden-Fowler equation
- Gaussian integrations.
MSC
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