Solving Nonlinear Partial Differential Equations By Using Adomian Decomposition Method, Modified Decomposition Method And Laplace Decomposition Method

Abstract

In this paper, we consider mostly the inhomogeneous Fitzhugh-Nagumo-Huxley equation with its initial value. Adomian Decomposition Method (ADM), Modified Decomposition Method (MDM) and Laplace Decomposition Method (LDM) are applied to this equation to obtain the solution that satisfies the given initial condition. It can be easily seen that each method gives the exactly same solution. And then, the inhomogeneous Boussinesq equation and another nonlinear partial differential equation subject to given initial values are solved by using LDM. In applications of the methods, it is demonstrated that we get the solution with a fast convergence by using the advantage of the noise terms. Moreover, we do not need to turn the nonlinear terms into linear ones since Adomian polynomials are used. Therefore, it is deduced that these methods are, indeed, effective and suitable for the nonlinear partial differential equations with the initial values.

Keywords

• laplace decomposition method
• adomian decomposition method
• modified decomposition method
• fitzhugh- nagumo-huxley equation and the noise terms
• adomian ayrışma metodu
• değiştirilmiş ayrışma metodu
• laplace ayrışma metodu
• fitzhughnagumo-huxley denklemi and parazit terimler