In oil industry, spontaneous imbibition is an important phenomenon in recovery from fractured reservoirs which can be defined as spontaneous uptake of a wetting fluid into a porous solid. Spontaneous imbibition involves both cocurrent and countercurrent flows. When a matrix block is partially covered by water, oil recovery is dominated by cocurrent imbibition i.e. the production of non wettin...

in this paper, we consider non-linear ginsburg-pitaevski-gross equation with the rosen-morse and modifiedwoods-saxon potentials which is corresponding to the quantum vortices and has important applications in turbulence theory. we use the runge- kutta-fehlberg approximation method to solve the resulting non-linear equation.

the extended homogeneous balance method is used to construct exacttraveling wave solutions of the maccari system, in which thehomogeneous balance method is applied to solve the riccati equationand the reduced nonlinear ordinary differential equation. many exacttraveling wave solutions of the maccari system equation aresuccessfully obtained.

In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a ...

In this paper we consider the exact WKB analysis of a second-order non-homogeneous linear ordinary differential equation with a large parameter. We give a geometric criterion which guarantees the Borel summability of formal solutions of a non-homogeneous equation; this criterion is described in terms of exact steepest descent paths introduced in [AKT2]. An example related to the BNR equation ([...

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...

The relations between solutions of the three types of totally linear partial differential equations of first order are presented. The approach is based on factorization of a non-homogeneous first order differential operator to products consisting of a scalar function, a homogeneous first order differential operator and the reciprocal of the scalar function. The factorization procedure is utiliz...