Title : Study on approximate analytical techniques with its applications for engineers & scientists
Abstract:
The study deals with combined form of Elzaki transform and Adomian decomposition method. Nonlinear terms can be defined by adomian polynomials. The Elzaki transform is known for its advantage in solving linear ODE & PDE and integral equations [8,9,10] and the Adomian's decomposition method is a well-known method for solving linear and nonlinear, homogeneous and nonhomogeneous differential [2,1] and partial differential equations, integro-differential and fractional differential equations that gives exact solutions in form of a convergent series. The Convection–diffusion equation is a combination of diffusion and convection equation. In applied sciences and engineering field, these kind of problems appears regularly.
This approach gives approximate analytical solution of linear and non-linear convection-diffusion equations. The convection–diffusion equation is describing flows or stochastically-changing system. In biology, the reaction–diffusion–advection equation is used to model chemotaxis observed in bacteria, population migration and evolutionary adaptation to changing environments, etc. To test the proficiency and effectiveness of the method, we discuss here some cases. The primary goal of the paper is to apply an Elzaki Transform Decomposition Method to remove disadvantage of existing methods. So that we are applying Elzaki Transform Decomposition (EDM) Method for solving these kind of equations. Using EDM we get rapidly the exact solution of the considered equations. In this paper, the Elzaki transform and Adomian decomposition method have been applied to solve convection diffusion equations. The proposed method is powerful and efficient in finding the approximate analytical solutions and is applied without using linear approximation, discretization or restrictive hypothesis. By comparison with other methods like DTM, HPTM, VIM, solutions are matched which justified the implementation of the proposed method.
