An efcient algorithm to solve damped forced oscillator problems by Bernoulli operational matrix of integration
Singh, M., Sharma, S., Rawan, S. (2021). An efcient algorithm to solve damped forced oscillator problems by Bernoulli operational matrix of integration. EKB Journal Management System, 29(1), 1-11. doi: 10.1186/s42787-021-00115-w
Mithilesh Singh; Seema Sharma; Sunil Rawan. "An efcient algorithm to solve damped forced oscillator problems by Bernoulli operational matrix of integration". EKB Journal Management System, 29, 1, 2021, 1-11. doi: 10.1186/s42787-021-00115-w
Singh, M., Sharma, S., Rawan, S. (2021). 'An efcient algorithm to solve damped forced oscillator problems by Bernoulli operational matrix of integration', EKB Journal Management System, 29(1), pp. 1-11. doi: 10.1186/s42787-021-00115-w
Singh, M., Sharma, S., Rawan, S. An efcient algorithm to solve damped forced oscillator problems by Bernoulli operational matrix of integration. EKB Journal Management System, 2021; 29(1): 1-11. doi: 10.1186/s42787-021-00115-w

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

Journal of the Egyptian Mathematical Society
Volume 29, Issue 1, 2021, Pages 1-11    PDF (2.05 M)
Document Type: Original Article
DOI: 10.1186/s42787-021-00115-w
Authors
Mithilesh Singh1; Seema Sharma2; Sunil Rawan* 3
1Rajkiya Engineering College, Churk, Sonbhadra, Uttar Pradesh, India.
2Gurukula Kangri Vishwavidyalaya (Kanya Gurukula Campus), Haridwar, Uttarakhand, India.
3Gurukula Kangri Vishwavidyalaya, Haridwar, Uttarakhand, India.
Abstract
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 diferent problems of spring are
given to delineate the performance and perfection of this approach and compared the
results with the exact solution.
Keywords
: Orthonormal Bernoulli polynomials; Operational matrix; Damped forced oscillator problem
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