A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator

A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator

An efficient technique is proposed to solve the one-dimensional Burgers’ equation based on multiquadric radial basis function (MQ-RBF) for space approximation and a Lie-Group scheme for time integration. The comparisons of the numerical results obtained for different values of kinematic viscosity ar...

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Bibliographic Details
Main Author: Muaz Seydaoğlu
Format: Article
Language:English
Published: MDPI AG 2019-01-01
Series:Mathematics
Subjects:
Burgers’ equation
meshless method
multiquadric radial basis function (MQ-RBF)
Lie-group method
Online Access:https://www.mdpi.com/2227-7390/7/2/113
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spelling doaj-50ae328f07b4447b8803e1cda7dd50522020-11-24T21:33:28ZengMDPI AGMathematics2227-73902019-01-017211310.3390/math7020113math7020113A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group IntegratorMuaz Seydaoğlu0Department of Mathematics, Faculty of Art and Science, Muş Alparslan University, 49100 Muş, TurkeyAn efficient technique is proposed to solve the one-dimensional Burgers’ equation based on multiquadric radial basis function (MQ-RBF) for space approximation and a Lie-Group scheme for time integration. The comparisons of the numerical results obtained for different values of kinematic viscosity are made with the exact solutions and the reported results to demonstrate the efficiency and accuracy of the algorithm. It is shown that the numerical solutions concur with existing results and the proposed algorithm is efficient and can be easily implemented.https://www.mdpi.com/2227-7390/7/2/113Burgers’ equationmeshless methodmultiquadric radial basis function (MQ-RBF)Lie-group method
collection DOAJ
language English
format Article
sources DOAJ
author Muaz Seydaoğlu
spellingShingle Muaz Seydaoğlu
A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator
Mathematics
Burgers’ equation
meshless method
multiquadric radial basis function (MQ-RBF)
Lie-group method
author_facet Muaz Seydaoğlu
author_sort Muaz Seydaoğlu
title A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator
title_short A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator
title_full A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator
title_fullStr A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator
title_full_unstemmed A Meshless Method for Burgers’ Equation Using Multiquadric Radial Basis Functions With a Lie-Group Integrator
title_sort meshless method for burgers’ equation using multiquadric radial basis functions with a lie-group integrator
publisher MDPI AG
series Mathematics
issn 2227-7390
publishDate 2019-01-01
description An efficient technique is proposed to solve the one-dimensional Burgers’ equation based on multiquadric radial basis function (MQ-RBF) for space approximation and a Lie-Group scheme for time integration. The comparisons of the numerical results obtained for different values of kinematic viscosity are made with the exact solutions and the reported results to demonstrate the efficiency and accuracy of the algorithm. It is shown that the numerical solutions concur with existing results and the proposed algorithm is efficient and can be easily implemented.
topic Burgers’ equation
meshless method
multiquadric radial basis function (MQ-RBF)
Lie-group method
url https://www.mdpi.com/2227-7390/7/2/113
work_keys_str_mv AT muazseydaoglu ameshlessmethodforburgersequationusingmultiquadricradialbasisfunctionswithaliegroupintegrator
AT muazseydaoglu meshlessmethodforburgersequationusingmultiquadricradialbasisfunctionswithaliegroupintegrator
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