B-polynomial multiwavelets approach for the solution of Abel's integral equation

Abstract

A numerical method for solving Abel's integral equation as singular Volterra integral equations is presented. The method is based upon Bernstein polynomial (B-polynomial) multiwavelet basis approximations. The properties of B-polynomial multiwavelets are first presented. These properties are then utilized to reduce the singular Volterra integral equations to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Keywords:

• Bernstein polynomial
• multiwavelets
• Abel's integral equations
• Volterra integral equations

2000 AMS Subject Classification :

• 45D05
• 45E10
• 65R20
• 65D99
• 42A15

Acknowledgements

The author would like to thank one of the reviewers for comments and suggestions which have improved the paper highly. This research is supported by Shahid Beheshti University and the author thanks Shahid Beheshti University for this support.