An efficient algorithm to solve damped forced oscillator problems by Bernoulli operational matrix of integration
- Resource Type
- article
- Authors
- Mithilesh Singh; Seema Sharma; Sunil Rawan
- Source
- Journal of the Egyptian Mathematical Society, Vol 29, Iss 1, Pp 1-11 (2021)
- Subject
- Orthonormal Bernoulli polynomials
Operational matrix
Damped forced oscillator problem
Mathematics
QA1-939
- Language
- English
- ISSN
- 2090-9128
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 different problems of spring are given to delineate the performance and perfection of this approach and compared the results with the exact solution.