Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

Knowledge of permeability is critical for developing an effective reservoir description. Permeability data may be calculated from well tests, cores and logs. Normally, using well log data to derive estimates of permeability is the lowest cost method. This paper will focus on the evaluation of formation permeability in un-cored intervals for Abughirab field/Asmari reservoir in Iraq from core and well log data. Hydraulic flow unit (HFU) concept is strongly related to the flow zone indicator (FZI) which is a function of the reservoir quality index (RQI). Both measures are based on porosity and permeability of cores. It is assumed that samples with similar FZI values belong to the same HFU. A generated method is also used to calculate permea

          In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

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In this paper, we consider a new approach to solve type of partial differential equation by using coupled Laplace transformation with decomposition method to find the exact solution for non–linear non–homogenous equation with initial conditions. The reliability for suggested approach illustrated by solving model equations such as second order linear and nonlinear Klein–Gordon equation. The application results show the efficiency and ability for suggested approach.

In this paper, a new analytical method is introduced to find the general solution of linear partial differential equations. In this method, each Laplace transform (LT) and Sumudu transform (ST) is used independently along with canonical coordinates. The strength of this method is that it is easy to implement and does not require initial conditions.

Significant advances in horizontal well drilling technology have been made in recent years. The conventional productivity equations for single phase flowing at steady state conditions have been used and solved using Microsoft Excel for various reservoir properties and different horizontal well lengths.
The deviation between the actual field data, and that obtained by the software based on conventional equations have been adjusted to introduce some parameters inserted in the conventional equation.
The new formula for calculating flow efficiency was derived and applied with the best proposed values of coefficients ψ=0.7 and ω= 1.4. The simulated results fitted the field data.
Various reservoir and field parameters including late