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 article, the nonlinear problem of Jeffery-Hamel flow has been solved analytically and numerically by using reliable iterative and numerical methods. The approximate solutions obtained by using the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM). The obtained solutions are discussed numerically, in comparison with other numerical solutions obtained from the fourth order Runge-Kutta (RK4), Euler and previous analytic methods available in literature. In addition, the convergence of the proposed methods is given based on the Banach fixed point theorem. The results reveal that the presented methods are reliable, effective and applicable to solve other nonlinear problems.

     In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.

Because the Coronavirus epidemic spread in Iraq, the COVID-19 epidemic of people quarantined due to infection is our application in this work. The numerical simulation methods used in this research are more suitable than other analytical and numerical methods because they solve random systems. Since the Covid-19 epidemic system has random variables coefficients, these methods are used. Suitable numerical simulation methods have been applied to solve the COVID-19 epidemic model in Iraq. The analytical results of the Variation iteration method (VIM) are executed to compare the results. One numerical method which is the Finite difference method (FD) has been used to solve the Coronavirus model and for comparison purposes. The numerical simulat

The Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solutions for travelling waves of 

The present work involved preparation of new substituted and unsubstituted and poly imides (1-17) using reaction of acryloyl chloride with different amides (aliphatic ,aromatic) in the presence of a suitable solvent and amount tri ethyl amine (Et3N) with heating – the structure confirmation of all polymers were proved using FT-IR,1H-NMR,C13NMR and UV spectroscopy ,thermal analysis (TG) for some polymers confirmed their thermal stabilities . Other physical properties including softening and melting points, PH and solubility of the polymers were also measured

Green synthesis methods have emerged as favorable techniques for the synthesis of nano-oxides due to their simplicity, cost-effectiveness, eco-friendliness, and non-toxicity. In this study, Nickel oxide nanoparticles (NiO-NPs) were synthesized using the aqueous extract of Laurus nobilis leaves as a natural capping agent. The synthesized NiO-NPs were employed as an adsorbent for the removal of Biebrich Scarlet (BS) dye from aqueous solution using adsorption technique. Comprehensive characterization of NiO-NPs was performed using various techniques such as atomic force microscopy (AFM), Fourier transform infrared (FTIR), X-ray diffraction (XRD), Brunauer-Emmett and Teller (BET) analysis, and scanning electron microscopy (SEM). Additionally, o