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Solution of Fuzzy Volterra Integral Equations In A Bernstein Polynomial Basis

Maryam Mosleh1 and Mahmood Otadi1
Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran

Abstract— In this paper, we have used the parametric form of fuzzy number and convert a fuzzy Volterra integral equation to a system of integral equations in crisp case. We present a numerical method for solving fuzzy Volterra integral equations of the second kind. The proposed method is based on approximating unknown function with Bernstein’s approximation. This method using simple computation with quite acceptable approximate solution. However, accuracy and efficiency are dependent on the size of the set of Bernstein polynomials. Furthermore we get an estimation of error bound for this method.

Index Terms— Fuzzy integral equations, System of Volterra integral equation, Bernstein polynomial

Cite: Maryam Mosleh and Mahmood Otadi, "Solution of Fuzzy Volterra Integral Equations In A Bernstein Polynomial Basis," Journal of Advances in Information Technology, Vol. 4, No. 3, pp. 148-155, August, 2013.doi:10.4304/jait.4.3.148-155