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<p>We establish constructive necessary and sufficient conditions for the solvability and propose a scheme for the construction of solutions of a nonlinear boundary-value problem unsolved with respect to the derivative. On the basis of the Adomian decomposition method, we construct convergent iterative schemes aimed at finding approximations to the solutions of a nonlinear boundary-value problem unsolved with respect to the derivative. As examples of application of the proposed iterative scheme, we find approximations to the solutions of a periodic boundary-value problem for Rayleigh-type equations unsolved with respect to the derivative including the case of a periodic problem for the equation that determines the motion of a satellite along an elliptic orbit.</p>

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ADOMIAN DECOMPOSITION METHOD IN THE THEORY OF NONLINEAR BOUNDARY-VALUE PROBLEMS UNSOLVED WITH RESPECT TO THE DERIVATIVE

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • Peter Benner,
  • Sergii Chuiko,
  • Olga Nesmelova

摘要

We establish constructive necessary and sufficient conditions for the solvability and propose a scheme for the construction of solutions of a nonlinear boundary-value problem unsolved with respect to the derivative. On the basis of the Adomian decomposition method, we construct convergent iterative schemes aimed at finding approximations to the solutions of a nonlinear boundary-value problem unsolved with respect to the derivative. As examples of application of the proposed iterative scheme, we find approximations to the solutions of a periodic boundary-value problem for Rayleigh-type equations unsolved with respect to the derivative including the case of a periodic problem for the equation that determines the motion of a satellite along an elliptic orbit.