Euler wavelets operational matrix of integration and its application in the calculus of variations

ABSTRACT

In this paper, a Euler wavelets method for solving the variational problems is presented. The operational matrices of integration and product of Euler wavelets are calculated. Then, by using Euler wavelets and the operational matrices, the variational problems are reduced into the system of algebraic equations. Furthermore, the convergence analysis and error bound of the Euler wavelets method are given. Some examples are included to demonstrate the applicability and validity of the schemes.

KEYWORDS:

• Euler wavelets
• operational matrix of integration
• calculus of variational
• numerical solutions
• convergence analysis

2020 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 49M05
• 65K10

Acknowledgments

The authors are very grateful to the reviewers for giving valuable suggestions and comments which significantly contributed to the quality and presentation of the paper.

Disclosure statement

The authors declare that they have no competing interests.

Additional information

Funding

The research is supported by the Natural Science Foundation of Ningbo City, China (No. 2021J143, 2021J144).