New technique to avoid "noise terms" on the solutions of inhomogeneous differential equations by using Adomian decomposition method

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Abstract

In this paper we present a new technique to get the solutions of inhomogeneous differential equations using Adomian decomposition method (ADM) without noise terms. We construct an appropriate differential equations for the inhomogeneity function which must be contains the integral variable, and convert all of these differential equations (original differential equation and the constructed differential equations) to augmented system of first-order differential equations. The ADM is using to solve the augmented system and the initial conditions are taken as initial approximations. Generally, the closed form of the exact solution or its expansion is obtained without any noise terms. Several differential equations will be tested to confirm the newly developed technique.

Original languageEnglish
Pages (from-to)685-696
Number of pages12
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume14
Issue number3
DOIs
StatePublished - Mar 2009
Externally publishedYes

Keywords

  • Adomian decomposition method
  • Noise terms
  • Nonlinear differential equations

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