Equilibrium Integral Equations with Kurtosian Kernels in Spaces of Various Dimensions

Никитин, А. А.; Nikolaev, M. V.

doi:10.3103/s0278641918030093

Cited by 7 publications

(2 citation statements)

References 9 publications

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“…This allows reducing d-dimensional integrations to discrete Hankel [25] or Fourier-Bessel [26] transforms in one (radial) dimension by integrating analytically out all angle dependencies. The chief advantage of this approach is the fact that then the total number of operations becomes independent of d and remains the same (of order of N ln N) for any dimensionality [27], just as at d = 1.…”

Section: Discussionmentioning

confidence: 99%

Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps

2020

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An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point particles placed in $\mathbb {R}^{d} (d \geq 1)$ ℝ d ( d ≥ 1 ) . The particles perform random jumps with pair-wise repulsion in the course of which they can also merge. The kinetic equation is an essentially nonlinear and nonlocal integro-differential equation, which can hardly be solved analytically. The numerical algorithm which we use to solve it is based on a space-time discretization, boundary conditions, composite Simpson and trapezoidal rules, Runge-Kutta methods, and adjustable system-size schemes. We show that, for special choices of the model parameters, the solutions manifest unusual time behavior. A numerical error analysis of the obtained results is also carried out.

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Section: Discussionmentioning

confidence: 99%

Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps

2020

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“…This allows to reduce d-dimensional integrations to discrete Hankel [29] or Fourier-Bessel [30] transforms in one (radial) dimension by integrating analytically out all angle dependencies. The chief advantage of this approach is the fact that then the total number of operations becomes independent of d and remains the same (of order of N ln N) for any dimensionality [31], just as at d = 1.…”

Section: Discussionmentioning

confidence: 99%

Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps

Omelyan¹,

Kozitsky²,

Pilorz³

2020

Preprint

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An algorithm is proposed for finding numerical solutions of a kinetic equation that describes an infinite system of point articles placed in R d (d ≥ 1). The particles perform random jumps with pair wise repulsion, in the course of which they can also merge. The kinetic equation is an essentially nonlinear and nonlocal integro-differential equation, which can hardly be solved analytically. The derivation of the algorithm is based on the use of space-time discretization, boundary conditions, composite Simpson and trapezoidal rules, Runge-Kutta methods, adjustable system-size schemes, etc. The algorithm is then applied to the one-dimensional version of the equation with various initial conditions. It is shown that for special choices of the model parameters, the solutions may have unexpectable time behaviour. A numerical error analysis of the obtained results is also carried out.

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Application of the Leray-Schauder Principle to the Analysis of a Nonlinear Integral Equation

Nikolaev

Никитин

2019

Diff Equat

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Equilibrium Integral Equations with Kurtosian Kernels in Spaces of Various Dimensions

Cited by 7 publications

References 9 publications

Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps

Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps

Algorithm for numerical solutions to the kinetic equation of a spatial population dynamics model with coalescence and repulsive jumps

Application of the Leray-Schauder Principle to the Analysis of a Nonlinear Integral Equation

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