Second-order two-point boundary value problems using the variational iteration algorithm-II

Abstract

In this paper, we introduce an improved variational iteration method (VIM) for nonlinear second-order boundary value problems. The main advantage of this modification is that it can avoid additional computation in determining the unknown parameters in initial approximation when solving boundary value problems using the conventional VIM. Also, iterative sequences obtained using the improved VIM do satisfy the boundary conditions while iterative sequences obtained using conventional VIM may not, in general, satisfy the boundary conditions. Numerical results reveal that the improved method is accurate and efficient.

Keywords:

• improved variational iteration method
• nonlinear
• boundary value problems

2000 AMS Subject Classifications :

• 34K10
• 34B15

Acknowledgements

The authors would like to express their thanks to unknown referees for careful reading and helpful comments. Project supported by the National Natural Science Foundation of China (Grant No.10771044), the Natural Science Foundation of Heilongjiang province (Grant No. A06-05).