Adomian Decomposition Method for the One-dimensional Nonlocal Fisher–Kolmogorov–Petrovsky–Piskunov Equation

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Abstract

The Adomian decomposition method is applied to construct an approximate solution of the generalized one-dimensional Fisher–Kolmogorov–Petrovsky–Piskunov equation describing the population dynamics with nonlocal competitive losses. An approximate solution is constructed in the class of decreasing functions. The diffusion operator is taken as a reversible linear operator. The inverse operator is presented in terms of the diffusion propagator. An example of the approximate solution of the Cauchy problem for the function of competitive losses and for the initial function of the Gaussian type is considered.

Original languageEnglish
Pages (from-to)710-719
Number of pages10
JournalRussian Physics Journal
Volume62
Issue number4
DOIs
Publication statusPublished - 1 Aug 2019

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decomposition
linear operators
operators
Cauchy problem
propagation

Keywords

  • Adomian’s decomposition method
  • approximate solutions
  • diffusion propagator
  • nonlocal generalized Fisher–Kolmogorov–Petrovsky–Piskunov equation

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

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title = "Adomian Decomposition Method for the One-dimensional Nonlocal Fisher–Kolmogorov–Petrovsky–Piskunov Equation",
abstract = "The Adomian decomposition method is applied to construct an approximate solution of the generalized one-dimensional Fisher–Kolmogorov–Petrovsky–Piskunov equation describing the population dynamics with nonlocal competitive losses. An approximate solution is constructed in the class of decreasing functions. The diffusion operator is taken as a reversible linear operator. The inverse operator is presented in terms of the diffusion propagator. An example of the approximate solution of the Cauchy problem for the function of competitive losses and for the initial function of the Gaussian type is considered.",
keywords = "Adomian’s decomposition method, approximate solutions, diffusion propagator, nonlocal generalized Fisher–Kolmogorov–Petrovsky–Piskunov equation",
author = "Shapovalov, {A. V.} and Trifonov, {A. Yu}",
year = "2019",
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T1 - Adomian Decomposition Method for the One-dimensional Nonlocal Fisher–Kolmogorov–Petrovsky–Piskunov Equation

AU - Shapovalov, A. V.

AU - Trifonov, A. Yu

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Y1 - 2019/8/1

N2 - The Adomian decomposition method is applied to construct an approximate solution of the generalized one-dimensional Fisher–Kolmogorov–Petrovsky–Piskunov equation describing the population dynamics with nonlocal competitive losses. An approximate solution is constructed in the class of decreasing functions. The diffusion operator is taken as a reversible linear operator. The inverse operator is presented in terms of the diffusion propagator. An example of the approximate solution of the Cauchy problem for the function of competitive losses and for the initial function of the Gaussian type is considered.

AB - The Adomian decomposition method is applied to construct an approximate solution of the generalized one-dimensional Fisher–Kolmogorov–Petrovsky–Piskunov equation describing the population dynamics with nonlocal competitive losses. An approximate solution is constructed in the class of decreasing functions. The diffusion operator is taken as a reversible linear operator. The inverse operator is presented in terms of the diffusion propagator. An example of the approximate solution of the Cauchy problem for the function of competitive losses and for the initial function of the Gaussian type is considered.

KW - Adomian’s decomposition method

KW - approximate solutions

KW - diffusion propagator

KW - nonlocal generalized Fisher–Kolmogorov–Petrovsky–Piskunov equation

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