ANALYTICAL SOLUTION OF THE RELATIVISTIC KLEIN-GORDON WAVE EQUATION

In this study, the solution to Klein-Gordon equations with focus on analytical methods is discussed. The analytical methods used in this research are the Variational Iteration Method (VIM) developed by Ji-Huan He, Adomian Decomposition Method (ADM) by Adomian and New Iterative Method (NIM) developed by Daftardar Gejji and Jafari. The modified Adomian Decomposition method by Wazwaz was used to solve the linear inhomogeneous and nonlinear Klein-Gordon equations to accelerate the convergence of the solution and minimizes the size of calculation while still maintaining high accuracy of the analytical solution. All the problems considered yield the exact solutions with few iterations. The solutions obtained were compared with the exact solution and the solutions obtained by other existing methods. The solutions obtained by the three methods yield the same results and all the problems considered show that the Variational Iteration Method, Adomian Decomposition Method and New Iterative Method are very powerful and potent in solving Klein-Gordon equations and can be used to obtain closed form solutions of linear and nonlinear differential equations (ordinary and partial)

Numerical Solution of Coupled System of Nonlinear Partial Differential Equations Using Laplace-Adomian Decomposition Method

Aim of the paper is to investigate applications of Laplace Adomian Decomposition Method (LADM) on nonlinear physical problems. Some coupled system of non-linear partial differential equations (NLPDEs) are considered and solved numerically using LADM. The results obtained by LADM are compared with those obtained by standard and modified Adomian Decomposition Methods. The behavior of the numerical solution is shown through graphs. It is observed that LADM is an effective method with high accuracy with less number of components

A New Modification of Adomian Decomposition Method for Volterra Integral Equations of the Second Kind

We propose a new modification of the Adomian decomposition method for Volterra integral equations of the second kind. By the Taylor expansion of the components apart from the zeroth term of the Adomian series solution, this new technology overcomes the problems arising from the previous decomposition method. The validity and applicability of the new technique are illustrated through several linear and nonlinear equations by comparing with the standard decomposition method and the modified decomposition method. The results obtained indicate that the new modification is effective and promising

Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods

The modified decomposition method (MDM) and homotopy perturbation method (HPM) are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM) is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems