<p>An optimized decomposition technique for dealing with nonlinear differential equations was developed which provides an optimal design of the series solution based on the use of a linear interpolation of the nonlinear equation. In this paper, the Laplace transform and the optimized decomposition method are utilized to design an effective approach, namely the optimized Laplace decomposition method, to approximately solve nonlinear differential equations. The suggested method incorporates a linear approximation to the nonlinear equation, implements the Laplace transform and then designs an optimal decomposition of the series solution. Next, a modified version of the proposed method is formulated to deal with systems of nonlinear differential equations. Numerical simulations and comparisons are conducted to test the efficiency and performance of the suggested method. The performed simulation results confirmed that the suggested method produces wider convergence intervals and better accuracy compared to the Laplace decomposition method.</p>

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An optimized Laplace decomposition method for nonlinear differential equations in mathematical physics

  • Esraa El-Dababat,
  • Zaid Odibat

摘要

An optimized decomposition technique for dealing with nonlinear differential equations was developed which provides an optimal design of the series solution based on the use of a linear interpolation of the nonlinear equation. In this paper, the Laplace transform and the optimized decomposition method are utilized to design an effective approach, namely the optimized Laplace decomposition method, to approximately solve nonlinear differential equations. The suggested method incorporates a linear approximation to the nonlinear equation, implements the Laplace transform and then designs an optimal decomposition of the series solution. Next, a modified version of the proposed method is formulated to deal with systems of nonlinear differential equations. Numerical simulations and comparisons are conducted to test the efficiency and performance of the suggested method. The performed simulation results confirmed that the suggested method produces wider convergence intervals and better accuracy compared to the Laplace decomposition method.