Abstract
Approximate solutions of second-order non-linear ordinary differential equations containing a linear velocity dependent damping term and a small parameter of non-linearity are obtained with the aid of sets of orthogonal polynomials. The method of solution treats the effect of linear damping in such a way that the approximate solutions of the non-linear equations reduce to the exact solution of the corresponding linear problems as the small parameter of non-linearity tends to zero. Ultraspherical polynomials, which depend upon a parameter λ, the value of which is selected at the time of performing numerical calculations, are found to be efficacious for solving problems of engineering significance. Numerical calculations, based upon the approximate method for several values of λ and upon the fourth-order Runge-Kutta method of numerical intergration, for three non-linear equations, were performed and results were compared. It was found that, in these cases, the calculations effected with λ=3/2 most nearly agreed with the Runge-Kutta calculations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.