Comparison for accurate solutions of nonlinear Hammerstein fuzzy integral equations

Prakash Kumar Sahu; Santanu Saha Ray

Vol. 21 No. 2 (2016)

Regular Articles

Comparison for accurate solutions of nonlinear Hammerstein fuzzy integral equations

Published 2016-06-06

Prakash Kumar Sahu
Santanu Saha Ray

Prakash Kumar Sahu
Senior Research Fellow Department of Mathematics National Institute of Technology Rourkela

Santanu Saha Ray
Department of Mathematics National Institute of Technology Rourkela-769008, India

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Abstract

In this paper, efficient numerical techniques have been proposed to solve nonlinear Hammerstein fuzzy integral equations. The proposed methods are based on Bernsteinpolynomials and Legendre wavelets approximation. Usually, nonlinear fuzzy integral equations are very difficult to solve both analytically and numerically. The present methods applied to the integral equations is reduced to solve the system of nonlinear algebraic equations. Again, this system has been solved by Newton’s method. The numerical results obtained by present methods have been compared with those of the homotopy analysis method. Illustrative examples have been discussed to demonstrate the validity and applicability of the presented methods.

Keywords

Bernstein polynomial, Legendre wavelets, Hammerstein integral equation

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Author Biography

Prakash Kumar Sahu

Senior Research Fellow

Department of Mathematics

National Institute of Technology

Rourkela-769008, Odisha, India

Santanu Saha Ray

Associate Professor

Department of Mathematics

National Institute of Technology

Rourkela