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International Theoretical Science Journal
Volume 57 >>> № 6 NOVEMBER — DECEMBER 2021
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UDC 519.6
I.V. Hariachevska1, D.O. Protektor2


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

 i.garyachevskaya@karazin.ua

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

 d.protector@karazin.ua

COMPUTER SIMULATION SYSTEM FOR NONLINEAR PROCESSES
DESCRIBED BY THE KORTEWEG-DE VRIES–BURGERS EQUATION

Abstract. The article discusses the computer simulation system of nonlinear processes described by the Korteweg-de Vries–Burgers equation. The numerical solution of the Korteweg-de Vries–Burgers differential equation is implemented 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.

Keywords: nonlinear one-dimensional Korteweg-de Vries–Burgers equation, computer simulation system, non-stationary boundary-value problem, meshless method, radial basis functions.


FULL TEXT

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