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Abstract
In this work, authors propose some modifications Adomian decomposition method to get some accurate closed form approximate or exact solutions of Duffing- and Li´enard-type nonlinear ordinary differential equations.Results obtained by the revised scheme have been exploited subsequently to derive constraints among parameters to get the solutions to be bounded. The present scheme appears to be efficient and may be regarded as the confluence of apparently different methods for getting exact solutions for a variety of nonlinear ordinary differential equations appearing as mathematical models in several physical processes.
Highlights
Nonlinear oscillation or solitary wave propagation are ubiquitous
Authors in [32, 33] showed that appropriate modifications in the traditional Adomian decomposition method (ADM) could provide exact solutions in compact form for a variety of nonlinear ordinary differential equations (NLODEs) involving single algebraic nonlinear interaction term. Such method has been designated as rapidly convergent approximation method (RCAM). This success encouraged us to explore whether an accurate closed-form approximate or exact solution of another family of NLODEs involving relatively difficult nonlinear interaction terms can be obtained in a compact form with the invention of further trick on the existing scheme of RCAM
The objective of this paper is to present an efficient scheme through some modifications on ADM to obtain an accurate closed-form approximate or exact solutions of DTE(1) and LTE(2)
Summary
Nonlinear oscillation or solitary wave propagation are ubiquitous. They model numerous physical phenomena: from condensed matter physics, nonlinear optics, plasma physics, fluid dynamics, etc. to biophysics. One of its important aspects, e.g. as a tool for getting an exact solution of the equation concerned, if that is integrable, has not been yet exercised rigorously In their attempt, authors in [32, 33] showed that appropriate modifications in the traditional ADM could provide exact solutions in compact form for a variety of nonlinear ordinary differential equations (NLODEs) involving single algebraic nonlinear interaction term. Authors in [32, 33] showed that appropriate modifications in the traditional ADM could provide exact solutions in compact form for a variety of nonlinear ordinary differential equations (NLODEs) involving single algebraic nonlinear interaction term Such method has been designated as rapidly convergent approximation method (RCAM).
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