Moving least squares collocation method for Volterra integral equations with proportional delay

ABSTRACT

In this work, we apply the moving least squares (MLS) method for numerical solution of Volterra integral equations with proportional delay. The scheme utilizes the shape functions of the MLS approximation constructed on scattered points as a basis in the discrete collocation method. The proposed method is meshless, since it does not require any background mesh or domain elements. An error bound is obtained to ensure the convergence and reliability of the method. Numerical results approve the efficiency and applicability of the proposed method.

KEYWORDS:

• MLS method
• Volterra integral equations
• proportional delay
• collocation
• numerical solution

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 45D05

Acknowledgements

The authors would like to express their sincere gratitude to Professor Sheng and anonymous referees who's valuable comments and recommendations improved the quality of this paper significantly.

Disclosure statement

No potential conflict of interest was reported by the authors.