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A variant of error estimates approximate solutions of the cauchy problem for nonlinear differential equations in the neighbourhood of the moving singularity in the complex plane

Pchelova Alevtina   (I. Yakovlev Chuvash State Pedagogical University )

The article considers a first-order nonlinear ordinary differential equation with moving singularity which cannot be solved in quadratures in general case. We use the approximate method for solving nonlinear differential equations with movable singular points of algebraic type proposed by V.N. Orlov. The existence and uniqueness of Cauchy problem solution for this equation in some neighborhood of moving singularity is formulated, the approximate solution of the equation in neighborhood of moving sin-gularity is constructed and research of influence of perturbation of moving singularity on the approximate solution is carried out. The results are ob-tained in a complex domain. Comparison of calculation results with simi-lar results of calculations obtained by the author earlier is given.

Keywords:nonlinear ordinary differential equation, movable singular point, Cauchy problem, approximate analytical solution, perturbation, error estimation.
 

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Citation link:
Pchelova A. A variant of error estimates approximate solutions of the cauchy problem for nonlinear differential equations in the neighbourhood of the moving singularity in the complex plane // Современная наука: актуальные проблемы теории и практики. Серия: Естественные и Технические Науки. -2017. -№12. -С. 61-65
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