Numerical treatment of nonlinear Volterra integral equations of Urysohn type with proportional delay

ABSTRACT

Although mesh-less methods such as RBFs owe their fame to the advantage in dealing with multi-dimensional problems, we show that they are efficient tools for solving nonlinear Volterra integral equations with proportional delay. The error estimate is provided, and it is tested via a few numerical experiments. It demonstrates the efficiency and applicability of the proposed method.

KEYWORDS:

• Volterra integral equations
• Urysohn type
• proportional delay
• mesh-less method
• radial basis functions

2000 MSC CLASSIFICATION:

• 45G10

Acknowledgments

The authors are grateful to Professor Lai, associate editor and anonymous referees for their valuable comments and recommendations which improved the quality of this work significantly.

Disclosure statement

No potential conflict of interest was reported by the authors.