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Numerical Analysis and Computation Commons™
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Full-Text Articles in Numerical Analysis and Computation
Homotopy Perturbation Method With Two Expanding Parameters, Ji-Huan He
Homotopy Perturbation Method With Two Expanding Parameters, Ji-Huan He
Ji-Huan He
A homotopy perturbation method with two expanding parameters is suggested. The method is especially effective for a nonlinear equation with two nonlinear terms, which might have different effects on the solution. A nonlinear oscillator is used as an example to elucidate the solution procedure.
Fractional Calculus For Nanoscale Flow And Heat Transfer, Hong-Yan Liu, Ji-Huan He, Zheng-Biao Li
Fractional Calculus For Nanoscale Flow And Heat Transfer, Hong-Yan Liu, Ji-Huan He, Zheng-Biao Li
Ji-Huan He
Purpose – Academic and industrial researches on nanoscale flows and heat transfers are an area of increasing global interest, where fascinating phenomena are always observed, e.g. admirable water or air permeation and remarkable thermal conductivity. The purpose of this paper is to reveal the phenomena by the fractional calculus. Design/methodology/approach – This paper begins with the continuum assumption in conventional theories, and then the fractional Gauss’ divergence theorems are used to derive fractional differential equations in fractal media. Fractional derivatives are introduced heuristically by the variational iteration method, and fractal derivatives are explained geometrically. Some effective analytical approaches to fractional …