Modified Adomian decomposition method for specific second order ordinary differential equations

On Discrete Adomian Decomposition Method with Chebyshev Abscissa for Nonlinear Integral Equations of Hammerstein Type

“…Then, discrete the independent variable at the nodes us sion of the in ed for the quadrature rule in Equation (14). Quadrature rules that are based on an expan tegrand in terms of Chebyshev polynomials employ a  change of variables and use a discrete cosine transform approximation for the cosine series which have fast converging accuracy comparable to another quadrature rules.…”

“…There are significant interest in applying Adomian decomposition method (ADM) for a wide class of nonlinear equations. For example, ordinary and partial differential equations, integral equations and integro-differential equations, see [13][14][15][16] and references therein.…”

New Adomian’s Polynomials Formulas for the Non-linear and Nonautonomous Ordinary Differential Equations

“…The previous works concerning this method deal only with the case of non-linear autonomous differential equation see [16][17][18][19][20][21][22][23][24][25][26][27]. In this paper, this technique is applied to non-linear and non-autonomous differential equations.…”

Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics

“…MDM was first developed by Wazwaz and El-Seyed [1] who applied it to solve the ordinary differential equations (ODEs). Since then the MDM has been used for solving various equations in mathematics and physics [2][3][4], boundary value problems [5][6][7][8][9], various problems in engineering [10][11][12][13], and initial-value problems [14][15][16][17]. Adomian et al [14] solved the Lane-Emden equation using the MDM.…”