in this paper at first , we discuss about nonlinear pseudoparabolic equations with nonlocalboundary conditions and their results.at second we use an effective error estimation for this method altough has not yet beendiscussed. the aim of this paper is to fill this gap.

existence of periodic solutions for non-linear third order autonomous differential equation (o.d.e.) has not been investigated to as large an extent as non-linear second order. the popular poincare-bendixon theorem applicable to second order equation is not valid for third order equation (see [3]). this conclusion opens a way for further investigation.

We address the small-time evolution of interfaces (fronts) for the pseudoparabolic generalization ∂u ∂t = ∂ ∂x ( u ∂u ∂x + u ∂2u ∂x∂t ) of the porous-medium equation, identifying regimes in which the local behavior remains fixed for some finite time and others in which it changes instantaneously. A number of phenomena beyond those exhibited by the porous-medium equation are elucidated, includin...