Numerical approach for solving linear Fredholm integro-differential equation with piecewise intervals by Bernoulli polynomials

ABSTRACT

In this paper a numerical method is given for the solution of linear Fredholm integro-differential equation (FIDE) with piecewise intervals under the mixed conditions using the Bernoulli polynomials. The aim of this article is to present an efficient numerical procedure for solving linear FIDE with piecewise intervals. This method transforms linear FIDE with piecewise intervals and the given conditions into matrix equation which corresponds to a system of linear algebraic equation. Finally, some experiments and their numerical solutions are given. The results reveal that this method is reliable and efficient.

KEYWORDS:

• Fredholm integro-differential equation
• Bernoulli polynomials
• numerical solutions
• polynomial approximations

2010 AMS SUBJECT CLASSIFICATIONS:

• 34A08
• 26A33
• 41A58
• 33F05

Disclosure statement

No potential conflict of interest was reported by the authors.