Decomposition method for the Camassa–Holm equation

Decomposition Method for Camassa-holm Equation

Restarted Adomian’s Decomposition Method for Duffing’s Equation

The Adomian’s decomposition method (ADM) is a solution method with a wide range of applications including the solution of algebraic, differential, integral and integro-differential equations or system of equations. This method was first introduced by Adomian [1, 2] in the beginning of the 1980’s. In this method the solution is considered as an rapidly converging, infinite series. The convergenc...

The Modified Decomposition Method for the Boussinesq Equation

In this paper, the modified decomposition method is used to solve the generalized Boussinesq equation. This equation commonly describes the propagation of small amplitude long waves in several physical contents. The exact solution of the equation is obtained by the modified decomposition method in the form of a convergent series with easily computable components and, moreover, the convergence a...

The Adomian decomposition method for solving delay differential equation

A numerical method based on the Adomian decomposition method which has been developed by Adomian [Adomian, G. (1994). Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Publishers, Boston, MA] is introduced in this paper for the approximate solution of delay differential equation (DDE). The algorithm is illustrated by studying an initial value problem. The results o...

A Domain Decomposition Method for Time Fractional Reaction-Diffusion Equation

The computational complexity of one-dimensional time fractional reaction-diffusion equation is O(N²M) compared with O(NM) for classical integer reaction-diffusion equation. Parallel computing is used to overcome this challenge. Domain decomposition method (DDM) embodies large potential for parallelization of the numerical solution for fractional equations and serves as a basis for distributed, ...