ADM and Its Modification for Solving PDEs. Decomposition Method and its Modification for Solving Partial Differential Equations

      Аннотация: A comparison study between decomposition method and its modification for solving different kinds of PDEs is presented. To demonstrate how these decomposition methods are effective and reliable for solving the non-linear PDEs, solutions of some its kinds subjected to initial conditions are attained by these methods. In the application of the methods, it is clearly noticed that there is no need to convert the nonlinear terms into the linear ones due to the Adomian polynomials. In addition to this simplicity, it is seen that each method gives the same exact solution with variant time of implementation, rapid convergent solution series, and computational calculus. When the exact solution is not reached, we use truncated series. If the truncated series may be inaccurate in many regions. In order to enlarge the convergence domain of the truncated series, Laplace transform to the Adomian’s series solution have been applied, and yielding good results. A new modification of decomposition method is proposed to overcome the computational difficulties, as well as a comparison of the results found to those found by other modifications.

Ключевые слова: PDEs, ADM, Decomposition method, Partial Differential Equations, Adomian Decomposition Method, Adomian Polynomials, Boundary conditions, boundary value problem, equations, He Polynomials, Laplace