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This paper presents an efficient approach for determining an approximate solution of system of first order differential equations with variable coefficients. It is introduced as a differential equation with piecewise constant arguments corresponding to the considered initial value problem, which depend on a positive integer number n. It is proved that this equation has a unique piecewise-smooth solution, which will be an approximate solution for the considered initial value problem for large n. Numerical results are given on examples showing the efficiency and high accuracy of the suggested method.

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Piecewise Constant Argument Method for Nonlinear Systems of Differential Equations

  • 会议论文

  • 发表日期：

    2025年

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  • Mukhiddin I. Muminov,
  • Zafar Z. Jumaev

摘要

This paper presents an efficient approach for determining an approximate solution of system of first order differential equations with variable coefficients. It is introduced as a differential equation with piecewise constant arguments corresponding to the considered initial value problem, which depend on a positive integer number n. It is proved that this equation has a unique piecewise-smooth solution, which will be an approximate solution for the considered initial value problem for large n. Numerical results are given on examples showing the efficiency and high accuracy of the suggested method.