Two-dimensional Legendre wavelet method for the numerical solutions of fuzzy integro-differential equations

Article type: Research Article

Authors: Sahu, Prakash Kumar | Saha Ray, Santanu

Affiliations: Department of Mathematics, National Institute of Technology Rourkela, Rourkela, Odisha, India

Note: [] Corresponding author. Santanu Saha Ray, Department of Mathematics, National Institute of Technology Rourkela, Rourkela-769008, Odisha, India. Tel.: +91 661 246 2709; Fax: +91 661 247 2926; E-mail: [email protected]

Abstract: In this paper, two dimensional Legendre wavelet method has been applied to solve the fuzzy integro-differential equations. The properties of Legendre wavelets are first presented. In fuzzy case, we have developed two dimensional Legendre wavelets to approximate the fuzzy integro-differential equations. The properties of Legendre wavelets are used to reduce the system of integral equations to a system of algebraic equations which can be solved by any usual numerical method. Illustrative examples have been discussed to demonstrate the validity and applicability of the present method.

Keywords: Legendre wavelets, legendre wavelet method, integro-differential equation, fuzzy number, fuzzy calculus

DOI: 10.3233/IFS-141412

Journal: Journal of Intelligent & Fuzzy Systems, vol. 28, no. 3, pp. 1271-1279, 2015