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.
@article{28349,
title = {Approximate Analytical Solution of a Third-Order IVP arising in Thin Film Flows driven by Surface Tension},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {35},
year = {2016},
doi = {10.5269/bspm.v35i3.28349},
language = {EN},
url = {http://dml.mathdoc.fr/item/28349}
}
Morlando, Fabrizio. Approximate Analytical Solution of a Third-Order IVP arising in Thin Film Flows driven by Surface Tension. Boletim da Sociedade Paranaense de Matemática, Tome 35 (2016) . doi : 10.5269/bspm.v35i3.28349. http://gdmltest.u-ga.fr/item/28349/