SOLVING NONLINEAR PDES USING THE HIGHER ORDER HAAR WAVELET METHOD ON NONUNIFORM AND ADAPTIVE GRIDS-Reference-Cited by-同舟云学术

SOLVING NONLINEAR PDES USING THE HIGHER ORDER HAAR WAVELET METHOD ON NONUNIFORM AND ADAPTIVE GRIDS

Published:2021-01-18 Issue:1 Volume:26 Page:147-169
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
language:
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Author:

Ratas Mart¹^ORCID,Salupere Andrus¹,Majak Jüri²^ORCID

Affiliation:

1. Department of Cybernetics, School of Science, Tallinn University of Technology, 12618 Tallinn, Estonia

2. Department of Mechanical and Industrial Engineering, School of Engineering, Tallinn University of Technology, 19086 Tallinn, Estonia

Abstract

The higher order Haar wavelet method (HOHWM) is used with a nonuniform grid to solve nonlinear partial differential equations numerically. The Burgers’ equation, the Korteweg–de Vries equation, the modified Korteweg–de Vries equation and the sine–Gordon equation are used as model equations. Adaptive as well as nonadaptive nonuniform grids are developed and used to solve the model equations numerically. The numerical results are compared to the known analytical solutions as well as to the numerical solutions obtained by application of the HOHWM on a uniform grid. The proposed methods of using nonuniform grid are shown to significantly increase the accuracy of the HOHWM at the same number of grid points.

Publisher

Vilnius Gediminas Technical University

Subject

Modeling and Simulation,Analysis

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