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

The Purpose of this study is mainly to improve the competitive position of products economic units using technique target cost and method reverse engineering and through the application of technique and style on one of the public sector companies (general company for vegetable oils) which are important in the detection of prices accepted in the market for items similar products and processing the problem of high cost which attract managerial and technical leadership to the weakness that need to be improved through the introduction of new innovative solutions which make appropriate change to satisfy the needs of consumers in a cheaper way to affect the decisions of private customer to buy , especially of purchase private economic units to

Research was conducted to study the effect of proline and aspirin with 10 and 20 ppm on seed germination and seedling growth of Lycopersicon esculentum and the effect of surface growth of Fusarium oxysporum. The results showed that the proline and aspirin effected significantly to decreased percentage of seed germination, acceleration of germination, promoter indicator, elongation speed of radical and plumule and also the infection percentage of seed decay and surface growth of Fusarium oxysporum was reduced significantly.

Research was conducted to study the effect of proline and aspirin with 10 and 20 ppm on seed germination and seedling growth of Lycopersicon esculentumand the effect of surface growthof Fusarium oxysporum.The results showed that the proline and aspirin effected significantly to decreased percentage of seed germination, acceleration of germination, promoter indicator, elongation speed of radical and plumule and also the infection percentage of seed decay and surface growth of Fusarium oxysporumwas reduced significantly.

In the present work, we use the Adomian Decomposition method to find the approximate solution for some cases of the Newell whitehead segel nonlinear differential equation which was solved previously with exact solution by the Homotopy perturbation and the Iteration methods, then we compared the results.