Accurate numerical solutions of conservative nonlinear oscillators

Nonlinear engineering: Modeling and application

article

Najeeb Alam Khan¹  Khan Nasir Uddin¹  Khan Nadeem Alam¹ 

[1] Department of Mathematical Sciences, University of Karachi

关键词: oscillator;    amplitude;    frequency;    Plasma;   

DOI  :  10.1515/nleng-2014-0009

来源: De Gruyter

【 摘 要 】

The objective of this paper is to present an investigation to analyze the vibration of a conservative nonlinear oscillator in the form u" + lambda u + u^(2n-1) + (1 + epsilon^2 u^(4m))^(1/2) = 0 for any arbitrary power of n and m. This method converts the differential equation to sets of algebraic equations and solve numerically. We have presented for three different cases: a higher order Duffing equation, an equation with irrational restoring force and a plasma physics equation. It is also found that the method is valid for any arbitrary order of n and m. Comparisons have been made with the results found in the literature the method gives accurate results.

【 授权许可】

Unknown