[PDF][PDF] A review of the Adomian decomposition method and its applications to fractional differential equations

JS Duan, R Rach, D Baleanu… - … in Fractional Calculus, 2012 - academia.edu
In this article we review the Adomian decomposition method (ADM) and its modifications
including different modified and parametrized recursion schemes, the multistage ADM for …

A new modification of the Adomian decomposition method for solving boundary value problems for higher order nonlinear differential equations

JS Duan, R Rach - Applied Mathematics and Computation, 2011 - Elsevier
In this paper we propose a new modified recursion scheme for the resolution of multi-order
and multi-point boundary value problems for nonlinear ordinary and partial differential …

Numerical computing to solve the nonlinear corneal system of eye surgery using the capability of Morlet wavelet artificial neural networks

BO Wang, JF Gomez-Aguilar, Z Sabir, MAZ Raja… - Fractals, 2022 - World Scientific
In this study, a novel heuristic computing technique is presented to solve bioinformatics
problem for the corneal shape model of eye surgery using Morlet wavelet artificial neural …

Unsupervised constrained neural network modeling of boundary value corneal model for eye surgery

M Umar, F Amin, HA Wahab, D Baleanu - Applied Soft Computing, 2019 - Elsevier
In this article, a numerical computing technique is developed for solving the nonlinear
second order corneal shape model (CSM) using feed-forward artificial neural networks …

Homotopy perturbation technique for solving two-point boundary value problems–comparison with other methods

C Chun, R Sakthivel - Computer Physics Communications, 2010 - Elsevier
The two-point boundary value problems occur in a wide variety of problems in engineering
and science. In this paper, we implement the homotopy perturbation method for solving the …

[HTML][HTML] A new modified Adomian decomposition method and its multistage form for solving nonlinear boundary value problems with Robin boundary conditions

JS Duan, R Rach, AM Wazwaz, T Chaolu… - Applied Mathematical …, 2013 - Elsevier
In this paper we propose a new modified recursion scheme for the resolution of boundary
value problems (BVPs) for second-order nonlinear ordinary differential equations with Robin …

Modified Adomian decomposition method and computer implementation for solving singular boundary value problems arising in various physical problems

M Kumar, N Singh - Computers & Chemical Engineering, 2010 - Elsevier
In this paper, we present an efficient numerical algorithm for solving singular two-point linear
and non-linear problems, which is based on the Modified Adomian Decomposition Method …

A soft computing approach based on fractional order DPSO algorithm designed to solve the corneal model for eye surgery

W Waseem, M Sulaiman, A Alhindi, H Alhakami - IEEE Access, 2020 - ieeexplore.ieee.org
In this research, a soft computing approach based on a Nature-inspired technique, the
Fractional-Order Darwinian Particle Swarm Optimization (FO-DPSO) algorithm, is hybridized …

A bibliography of the theory and applications of the Adomian decomposition method, 1961-2011

R Rach - Kybernetes, 2012 - emerald.com
I am pleased to submit my comprehensive worldwide bibliography on the Adomian
decomposition method:“A bibliography of the theory and applications of the Adomian …

Numerical solution of singular boundary value problems using Green's function and improved decomposition method

R Singh, J Kumar, G Nelakanti - Journal of Applied Mathematics and …, 2013 - Springer
In this work, an effective technique for solving a class of singular two point boundary value
problems is proposed. This technique is based on the Adomian decomposition method …