Weak periodic solutions of x? + 1 = 0 and the Harmonic Balance Method

8th Workshop on Multi-Rate Processes and Hysteresis;HSFS Workshop (Hysteresis and Slow-Fast Systems)

García-Saldaa, J.D.^1,2 ; Gasull, A.^1

Departament de Matemátiques, Universitat Autónoma, Barcelona Edifici C., Bellaterra, Barcelona

08193, Spain^1

Departamento de Matemática y Física Aplicadas, Facultad de Ingeniería, Universidad Católica, La Santísima Concepción. Casilla, Concepción

297, Chile^2

关键词: Harmonic Balance method;    Periodic solution;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/811/1/012003/pdf
DOI  :  10.1088/1742-6596/811/1/012003

来源: IOP

【 摘 要 】

We prove that the differential equation x + 1 = 0 has continuous weak periodic solutions and compute their periods. Then, we use the Harmonic Balance Method until order six to approximate these periods and to illustrate how the accuracy of the method increases with the order. Our computations rely on the Gröbner basis approach.