A new algorithm for calculating adomian polynomials for nonlinear operators

An Efficient Applications of Hes Variational Iteration Method Based on a Reliable Modification of Adomian Algorithm for Nonlinear Boundary Value Problems

“…This method is easy to implement and is more efficient than the Adomian method, also the lacks which mentioned in above there is not in this approach. Furthermore one famous example which was solved before by Liu and Wazwaz [15,16] is given to illustrate the performance of the method. Consider a specific non linear PDE [15,16] …”

“…Furthermore one famous example which was solved before by Liu and Wazwaz [15,16] is given to illustrate the performance of the method. Consider a specific non linear PDE [15,16] …”

“…• Wazwaz [15]applied Adomian method and obtained an infinite series which convergence to the exact solution. Compared with the [15], the present method has some obvious merits,for example the method is very straightforward, and the solution procedure can be done easily.…”

Approximate-analytical solutions of cable equation using conformable fractional operator

“…There are many studies on Adomian decomposition method (ADM) which can evaluate the solutions of FPDEs. The ADM has been applied to obtain approximate solutions of linear or nonlinear fractional differential equations, fractional ordinary differential equations (FODEs), FPDEs, integral and integro-differential equations [7,8,9,10,11,12,13,14,15]. Meanwhile, there are many applications of solution methods based on variational iteration method (VIM) to ordinary-partial differential equations and other research areas [16,17,18,19,20].…”

On the numerical solution of Korteweg–de Vries equation by the iterative splitting method

“…Many powerful methods have been presented, for instance, Darboux transformation method [9], Adomians decomposition method [15,11], He's perturbation method [16], Operator splitting method [10], Iterative splitting method [7].…”