Adomian decomposition method for a reliable treatment of the Bratu-type equations

By Abdul-Majid Wazwaz. Applied Mathematics and Computation, 2005

327 citations recorded by the source corpus.

Subfields: Mechanics of Materials, Modeling and Simulation, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e93d6ef2716143b2a0d19ec919b16596aea361fd

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In Mechanics of Materials

In Modeling and Simulation

In Statistical and Nonlinear Physics

Citations in the corpus

An algorithm based on the variational iteration technique for the Bratu-type and the Lane–Emden problems (2016, methodology): “Some other approximate analytical methods like Adomian decomposition method (ADM) [2,6], variational iteration method (VIM) [25], homotopy analysis method”
New Spectral Second Kind Chebyshev Wavelets Algorithm for Solving Linear and Nonlinear Second-Order Differential Equations Involving Singular and Bratu Type Equations (2013, methodology): “In recent years, it has been a popular testbed for numerical and perturbation methods [14–16].”
A Reliable Analytical Method for Solving Higher-Order Initial Value Problems (2013, methodology): “(46) We mention here that this RPS solution is the same as Adomian decomposition solution obtained in [41], homotopy perturbation solution obtained in [42], variational iteration solution obtained in [43], and perturbation-iteration solution obtained in [44].”
An efficient analytic approach for solving two‐point nonlinear boundary value problems by homotopy analysis method (2011, methodology): “The efficiency and reliability of the method is checked by its application to two important nonlinear exactly solvable differential equations namely nonlinear Troesch’s problem equation [37, 38] and strongly nonlinear Bratu’s equation [31, 34, 39], in addition to illustration exactly solvable differ”
A novel operational matrix method based on shifted Legendre polynomials for solving second-order boundary value problems involving singular, singularly perturbed and Bratu-type equations (2015, methodology): “In recent years, it has been a popular testbed for numerical and perturbation methods [21–27].”
The Lie-group shooting method for solving the Bratu equation (2011, methodology): “1, shows the plots of acceptable range of r signified by W(r) > 0 and A(r) for r 2 [0,1], which can be obtained from Eqs.”