Approximate Analytical Solution of a Third-Order IVP arising in Thin Film Flows driven by Surface Tension
DOI :
https://doi.org/10.5269/bspm.v35i3.28349Mots-clés :
Thin-lm ow, lubrication theory, surface tension, VIM.Résumé
In this paper, we present a way of applying the so-called He's variational iteration method (VIM) to numerically solve the non linear autonomous third-order ordinary dierential equation (ODE) y''' = y^-2 obtained by considering a traveling wave solution admitted by a lubrication equation modeling a two-dimensional spreading of a thin viscous lm on a inclined slope. Approximate analytical solution is derived and compared to the results obtained from the Adomian decomposition method (ADM) proposed in [20], to the exact analytical solution
[7,8], to a fth order Runge-Kutta method (DOPRI), a fourth order Runge-Kutta method (RK4), a three-stage fth order Runge-Kutta method (RKD5) developed in [18]. A very good agreement and accuracy is observed. Comparisons are obtained using symbolic capabilities of Maple 18.0 package.
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Publié
2016-10-25
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Research Articles
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