Weak form quadrature solution of 2mth-order Fredholm integro-differential equations

Abstract

A method is proposed for the solution of boundary-value problems of linear and non-linear $2m$th-order Fredholm integro-differential equations. A set of algebraic equations are obtained after introduction of Gauss–Lobatto quadrature and the generalized differential quadrature analog into the weak form description of a Fredholm integro-differential equation. Numerical examples are presented to demonstrate the reliability and high computational efficiency of the proposed method.

Keywords:

• Fredholm integro-differential equation
• numerical solution
• differential quadrature analog
• Gauss–Lobatto quadrature
• weak form

2010 AMS Subject Classifications:

• 45J05
• 65R20
• 65N30

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [Grant numbers 51178247 and 51378294].