An efficient algorithm to solve damped forced oscillator problems by Bernoulli operational matrix of integration

Journal of the Egyptian Mathematical Society

Seema Sharma¹  Sunil Rawan²  Mithilesh Singh³ 

[1] Gurukula Kangri Vishwavidyalaya (Kanya Gurukula Campus), Haridwar, Uttarakhand, India;Gurukula Kangri Vishwavidyalaya, Haridwar, Uttarakhand, India;Rajkiya Engineering College, Churk, Sonbhadra, Uttar Pradesh, India;

关键词: Orthonormal Bernoulli polynomials;    Operational matrix;    Damped forced oscillator problem;    65T60;    34A35;   

DOI  :  10.1186/s42787-021-00115-w

来源: Springer

【 摘 要 】

An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives was obtained in Yang and Srivastava (Commun Nonlinear Sci Numer Simul 29(1–3):499–504, 2015). In this paper, we obtain the numerical solution of damped forced oscillator problems by employing the operational matrix of integration of Bernoulli orthonormal polynomials. The operational matrix of integration is determined with the help of the integral operator on Bernoulli orthonormal polynomials. Numerical examples of two different problems of spring are given to delineate the performance and perfection of this approach and compared the results with the exact solution.

【 授权许可】

CC BY