A Novel Method for Nonlinear Impulsive Differential Equations in Broken Reproducing Kernel Space

Abstract

In this article, a new algorithm is presented to solve the nonlinear impulsive dif- ferential equations. In the first time, this article combines the reproducing kernel method with the least squares method to solve the second-order nonlinear impulsive differential equations. Then, the uniform convergence of the numerical solution is proved, and the time consuming Schmidt orthogonalization process is avoided. The algorithm is employed successfully on some numerical examples.

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Correspondence to Liangcai Mei 梅良才.

Additional information

This work is supported by a Young Innovative Talents Program in Universities and Colleges of Guangdong Province (2018KQNCX338), and two Scientific Research-Innovation Team Projects at Zhuhai Campus, Beijing Institute of Technology (XK-2018-15, XK-2019-10).

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Cite this article

Mei, L. A Novel Method for Nonlinear Impulsive Differential Equations in Broken Reproducing Kernel Space. Acta Math Sci 40, 723–733 (2020). https://doi.org/10.1007/s10473-020-0310-7

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Key words

  • Nonlinear impulsive differential equations
  • Broken reproducing kernel space
  • numerical algorithm

2010 MR Subject Classification

  • 97N40
  • 97R20