Mathematical Methods in the Applied Sciences · 2013 · 65 citations · 43 references
Natural SciencesMathematicsComputational MechanicsDifferential EquationsDynamical SystemsIntegral EquationsNumerical AlgorithmsNumerical AnalysisNumerical IntegrationNumerical Methods For Differential EquationsSystems Of Differential EquationsDifferential Equation SolversNumerical Methods For Integral EquationsVolterra EquationsVolterra Integral EquationsVolterra Theory
Abstract In this paper, we introduce systems of Volterra integral forms of the Lane–Emden equations. We use the systematic Adomian decomposition method to handle these systems of integral forms. The Volterra integral forms overcome the singular behavior at the origin x = 0. The Adomian decomposition method gives reliable algorithm for analytic approximate solutions of these systems. Our results are supported by investigating several numerical examples. Copyright © 2013 John Wiley & Sons, Ltd.
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Decomposition methods: A new proof of convergence
Y. Cherruault, G. Adomian · Mathematical and Computer Modelling · 1993 · 458 citations