Laplace Adomian Decomposition Method to study Chemical ion transport through soil

The paper deals with a theoretical study of chemical ion transport in soil under a uniform external force in the transverse direction, where the soil is taken as porous medium. The problem is formulated in terms of boundary value problem that consists of a set of partial differential equations, which is subsequently converted to a system of ordinary differential equations by applying similarity transformation along with boundary layer approximation. The equations hence obtained are solved by utilizing Laplace Adomian Decomposition Method (LADM). The merit of this method lies in the fact that much of simplifying assumptions need not be made to solve the non-linear problem. The decomposition parameter is used only for grouping the terms, therefore, the nonlinearities is handled easily in the operator equation and accurate approximate solution are obtained for the said physical problem. The computational outcomes are introduced graphically. By utilizing parametric variety, it has been demonstrated that the intensity of the external pressure extensively influences the flow behavior

New iterative technique for computing Fourier transforms.

The Fourier transformations have stimulated many amounts of articles in recent years. they arise in the fields of engineering, control systems, and technology like analyzing signals in electronic circuits, radio circuits, cell phones, image processing, and in solutions to heat transfer equations, Airy equations, Telegraph equations, Duffing equations, Wave equations, Fisher equations, Laplace equation, etc. In this paper, a new iterative method called Adomian Decomposition Method (ADM) is implemented to obtain the Fourier transform of functions by solving a linear ordinary differential equation of first order. This method focuses on finding Fourier transforms by knowing the series resulting from Adomian polynomials. Five famous examples are presented to test the effectiveness and validity of this technique. The results indicate that the accuracy of this method is fully in agreement with the classical method. Furthermore, when applying the Adomian decomposition method, we noticed that it provides accurate results and does not require a lot of time and effort to obtain Fourier transforms of the functions because it does not require a large number of iterations

An Examination Of The Effectiveness Of The Adomian Decomposition Method In Fluid Dynamic Applications

Since its introduction in the 1980\u27s, the Adomian Decomposition Method (ADM) has proven to be an efficient and reliable method for solving many types of problems. Originally developed to solve nonlinear functional equations, the ADM has since been used for a wide range of equation types (like boundary value problems, integral equations, equations arising in flow of incompressible and compressible fluids etc...). This work is devoted to an evaluation of the effectiveness of this method when used for fluid dynamic applications. In particular, the ADM has been applied to the Blasius equation, the Falkner-Skan equation, and the Orr-Sommerfeld equation. This study is divided into five Chapters and an Appendix. The first chapter is devoted to an introduction of the Adomian Decomposition method (ADM) with simple illustrations. The Second Chapter is devoted to the application of the ADM to generalized Blasius Equation and our result is compared to other published results when the parameter values are appropriately set. Chapter 3 presents the solution generated for the Falkner-Skan equation. Finally, the Orr-Sommerfeld equation is dealt with in the fourth Chapter. Chapter 5 is devoted to the findings and recommendations based on this study. The Appendix contains details of the solutions considered as well as an alternate solution for the generalized Blasius Equation using Bender\u27s delta-perturbation method