Computational and Applied Mathematics

, Volume 37, Supplement 1, pp 16–26

# A simple efficient method for solving sixth-order nonlinear boundary value problems

• Dang Quang A
• Dang Quang Long
Article

## Abstract

In this paper, we propose a simple efficient method for a sixth-order nonlinear boundary value problem. It is based on the reduction of the problem to an operator equation for the right-hand-side function. The existence and uniqueness of a solution and its positivity are established. An iterative method for finding the solution is investigated. A numerical realization of the iterative method with the use of a difference scheme of sixth-order accuracy shows the efficiency and advantages of the proposed method over some other methods.

## Keywords

Sixth-order boundary value problem Existence and uniqueness of solution Positivity of solution Iterative method

## Mathematics Subject Classification

65L10 65L20 34B15

## Notes

### Acknowledgements

We would like to thank the reviewers for their helpful comments for improving the quality of the paper. This work is supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the Grant number 102.01-2017.306.

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