Abstract
In this paper, we propose a new method to find the periodic solutions of differential equations. The key technique is to convert the problem of finding periodic solutions of differential equations into an optimization problem. Then by solving the corresponding optimization problem, we can find the periodic solutions of differential equations. Finally, some numerical results are presented to illustrate the utility of the technique.
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Communicated by R. Glowinski.
Supported by NSFC Grant 10801060, the Specialized Research Fund for the Doctoral Program of Higher Education (20070183052), the 985 Project of Jilin University, and the Science Research Foundation for Excellent Young Teachers of College of Mathematics at Jilin University. The authors thank Professor R. Glowinski and the anonymous referees for valuable suggestions and helpful comments.
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Feng, Z.X., Xu, X. & Ji, S.G. Finding the Periodic Solution of Differential Equation via Solving Optimization Problem. J Optim Theory Appl 143, 75–86 (2009). https://doi.org/10.1007/s10957-009-9544-1
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DOI: https://doi.org/10.1007/s10957-009-9544-1