Numerical integration, analytic continuation, and decomposition
Applied Mathematics and Computation
A new algorithm for calculating Adomian polynomials for nonlinear operators
Applied Mathematics and Computation
Linear and Nonlinear Integral Equations: Methods and Applications
Linear and Nonlinear Integral Equations: Methods and Applications
Decomposition methods: A new proof of convergence
Mathematical and Computer Modelling: An International Journal
Practical formulae for the calculus of multivariable adomian polynomials
Mathematical and Computer Modelling: An International Journal
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In this paper, we develop new numeric modified Adomian decomposition algorithms by using the Wazwaz-El-Sayed modified decomposition recursion scheme, and investigate their practicality and efficiency for several nonlinear examples. We show how we can conveniently generate higher-order numeric algorithms at will by this new approach, including, by using examples, 12th-order and 20th-order numeric algorithms. Furthermore, we show how we can achieve a much larger effective region of convergence using these new discrete solutions. We also demonstrate the superior robustness of these numeric modified decomposition algorithms including a 4th-order numeric modified decomposition algorithm over the classic 4th-order Runge-Kutta algorithm by example. The efficiency of our subroutines is guaranteed by the inclusion of the fast algorithms and subroutines as published by Duan for generation of the Adomian polynomials to high orders.