Analytical solution of a time-fractional Navier-Stokes equation by Adomian decomposition method

By Shaher Momani, Zaid M. Odibat. Applied Mathematics and Computation, 2006

426 citations recorded by the source corpus.

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/bfaba4b1fa66e1de018247dbe2d6165444abc026

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Citations in the corpus

The homotopy analysis method for solving the time-fractional Fornberg-Whitham equation and comparison with Adomian's decomposition method (2013, methodology): “These methods include the finite difference method [4–6], the Adams–Bashforth–Moulton method [7], the homotopy perturbation method (HPM) [8–10], the generalized differential transform method [11,12], the variational iteration method [13–15] and the Adomian’s decomposition method (ADM) [16,17].”
Algorithms for nonlinear fractional partial differential equations: A selection of numerical methods (2008, methodology): “The Adomian polynomial Ai can be calculated for all forms of nonlinearity according to specific algorithms constructed by Adomian [1], [14]–[18], [23].”
Numerical methods for nonlinear partial differential equations of fractional order (2008, background): “In these schemes, the solution takes the form of a convergent series with easily computable components.”
Invariant analysis of time fractional generalized Burgers and Korteweg–de Vries equations (2012, methodology): “As a consequence, several ad hoc methods such as the Finite difference method [16], Adomian decomposition method [17], Variational iteration method [18], Homotopy perturbation method [19], Laplace transformmethod [20], Fourier transformmethod [14], Generalized differential transformmethod [21]”
Analytical solution of fractional Navier–Stokes equation by using modified Laplace decomposition method (2014, methodology): “In this example, we consider the following time fractional Navier–Stokes equation [9] as:”
AN ALGORITHM FOR THE NUMERICAL SOLUTION OF DIFFERENTIAL EQUATIONS OF FRACTIONAL ORDER (2008, methodology): “The application of the two methods is successfully extended to obtain an analytical approximate solutions to linear and nonlinear differential equations of fractional order [24-28,32,45-47].”
Solving systems of fractional differential equations using differential transform method (2008, methodology): “Recently, theAdomian decomposition method and variational iteration method have been used for solving a wide range of problems [3,6,10–13,15–18,20].”