A Laplace decomposition algorithm applied to a class of nonlinear differential equations

By Suheil A. Khuri. 2001

377 citations recorded by the source corpus.

In this paper, a numerical Laplace transform algorithm which is based on the decomposition method is introduced for the approximate solution of a class of nonlinear differential equations. The technique is described and illustrated with some numerical examples. The results assert that this scheme is rapidly convergent and quite accurate by which it approximates the solution using only few terms of its iterative scheme.

Subfields: Computational Theory and Mathematics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0227e999aa3b1ea130f607afba90222e28fd110d

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In Computational Theory and Mathematics

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Homotopy perturbation transform method for nonlinear equations using He's polynomials (2011, methodology): “In previous papers [19,23,39–44]many authors have alreadyusedAdomianpolynomials to decompose the nonlinear terms in equations.”
Homotopy Analysis Sumudu Transform Method for Nonlinear Equations (2012, methodology): “[3,6,7,11,14,18,40], homotopy analysis method (HAM) [6,7,12,23,25,26,27,28,29,33], variational iteration method (VIM) [6,7,15,16,17,19], Laplace decomposition method (LDM) [20,24,37,41], homotopy perturbation transform method (HPTM) [22], homotopy perturbation sumudu transform method (HPSTM) [34] an”
Homotopy Perturbation Sumudu Transform Method for Nonlinear Equations (2011, methodology): “Various ways have been proposed recently to deal with these nonlinearities such as the Adomian decomposition method [39] and the Laplace decomposition algorithm [40-44].”
Sumudu Decomposition Method for Nonlinear Equations (2012, methodology): “Various powerful mathematical methods such as Adomian decomposition method (ADM) [1], homotopy perturbation method (HPM) [2], variational iteration method (VIM) [3, 4], Laplace decomposition method (LDM) [5, 6] and homotopy perturbation sumudu transform method (HPSTM) [7] have been proposed to obtai”