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Computer Simulation System for Nonlinear Processes Described By the Korteweg–de Vries–Burgers Equation

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Abstract

The article discusses the computer simulation system for nonlinear processes described by the Korteweg–de Vries–Burgers equation. The Korteweg–de Vries–Burgers differential equation numerically solved by the meshless approach using radial basis functions. The computer simulation system uses the following radial basis functions: Gaussian, multiquadric, inverse quadratic, inverse multiquadric, and Wu’s compactly-supported radial function. The solution of the nonlinear one-dimensional non-stationary Korteweg–de Vries–Burgers equation in the computer simulation system is visualized as a three-dimensional surface. The efficiency of the numerical solution in the computer simulation system is demonstrated by a benchmark problem for which numerical solutions were obtained, and the average relative error, average absolute error, and maximum error were calculated.

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Authors and Affiliations

  1. V. N. Karazin Kharkiv National University, Kharkiv, Ukraine

    I. V. Hariachevska & D. O. Protektor

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  1. I. V. Hariachevska
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  2. D. O. Protektor
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Correspondence to I. V. Hariachevska.

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Translated from Kibernetyka ta Systemnyi Analiz, No. 6, November–December, 2021, pp. 172–182.

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Hariachevska, I.V., Protektor, D.O. Computer Simulation System for Nonlinear Processes Described By the Korteweg–de Vries–Burgers Equation. Cybern Syst Anal 57, 998–1007 (2021). https://doi.org/10.1007/s10559-021-00425-y

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